t¦uû] lqdÏ utßm a±®vp · ckr £ltjûr (imp) eÚyôdÏm ùnvttôh¥p ªlÜm £\ltôlÜm brkr...
TRANSCRIPT
(i)
T¦Uû] LQdÏ UtßmA±®Vp
(Workshop Calculation and Science)NSQF
ØRp TÚYm
(1st Semester)
Aû]jÕ ùTô±«Vp ©¬ÜLÞdÏm
ùTôÕYô]Õ
(COMMON FOR All ENGINEERING TRADES)
T«t£jÕû\ ùTôÕ CVdLLm,§\uªÏ úUmTôÓ Utßm ùRô¯p Øû]úYôo AûUfNLm,
Ck§V AWÑ
úR£V ùRô¯tT«t£ FPLRVô¬l× ¨ûXVm, ùNuû]
RTôp ùTh¥ Gi 3142, £,¥,I. Y[ôLm, ¡i¥.ùNuû]- þ 600 032-
© NIMI, Not to be republished
(ii)
T¦Uû] LQdÏ Utßm A±®Vp (NSQF) ØRp TÚYm
Workshop Calculation and Science 1st Semester
Aû]jÕ ùTô±«Vp ©¬ÜLÞdÏm ùTôÕYô]Õ
Common for all Engineering Trades
T§l׬ûU © 2019 úR£V ùRô¯t T«t£ FPL RVô¬l× ¨ûXVm, ùNuû].
ØRtT§l× : Uôof 2019 ©W§Ls : 1000
Rs. 160/-
E¬ûU : úR£V ùRô¯t T«t£ FPL RVô¬l× ¨ûXVm, ùNuû].
úR£V ùRô¯t T«t£ FPL RVô¬l× ¨ûXVm, ùNuû]«u AàU§ CpXôUp CkR ©WÑWj§u
GkR Tϧ«û]Ùm , ÁiÓm ©WѬjRp ApXÕ GkR T¥Yj§Ûm SLp ùNnYÕ, ªu]Ô êXm
ApXÕ CVk§WêXm, úTôhúPô SLp, T§Ü ùNnRp ApXÕ RLYp úNªl× Utßm GkR
Y¯Øû\«Ûm §ÚmTl ùTßm YN§«û] ùNnVdáPôÕ.
ùY°ÂhPô[o
úR£V ùRô¯t T«t£ FPL RVô¬l× ¨ûXVm
ùTh¥ Gi: 3142, Uj§V ùRô¯t T«t£ Y[ôLm, ¡i¥ ùRô¯túThûP,
¡i¥, ùNuû] þ 600 032ùRôûXúT£ : 044þ2250 0248, 2250 0657, 2250 2421
ùRôûXSLp (Fax) : 91-44-2250 0791ªu AOóNp (Email) : [email protected], [email protected]
YûXR[m (Website) : www.nimi.gov.in
© NIMI, Not to be republished
(iii)
ØuàûW
Ck§V AWNôeLj§u úTWôYp CXdLô], 30 úLô¥ UdLÞdÏ, SôpYôõp JÚYÚdÏúYûX Ej§WYôRjûR 2020 Bi¥tÏs HtTÓjR úR£V §\u úUmTôhÓ ùLôsûLHtTÓjRlThÓs[Õ. §\u ªÏ ûL®û]OôóLû[ EÚYôdÏY§p ùRô¯t T«t£¨ûXVeLs (ITI) Ød¡V TeÏ YÏd¡\Õ. CdϱdúLô°u A¥lTûP«p RtLôXùRô¯tNôûXL°u úRûYdúLtT §\uªÏ ûL®û]OôóLû[ EÚYôd¡T«t£V°lTRtLôL ùRô¯tT«t£ TôP§hPj§û] (ITI syllabus) Uôt±VûUdL,ùRô¯tLp® T«tß]ôóLs, Lp®Vô[oLs Utßm TpúYß ©W§¨§Lû[ Es[Pd¡VJÚ ÏÝYô]Õ EÚYôdLlThPÕ. AdÏÝ®u TeÏRôWoL[ôL ùRô¯tNôûXL°p T¦×¬úYôo, ùRô¯p Øû]úYôo, Lp®Vô[oLs Utßm (ITI) -u ©W§¨§Ls APeÏYo.
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úR£V ùRô¯tT«t£ FPL RVôôõl× ¨ûXVjÕPu JÚe¡ûQkÕ EûZjÕ, ReLsTeL°lûT Sp¡ Cl×jRLm ùY°«P ER®V CVdÏ]ôó, Aû]jÕ Õû\ ©W§¨§Ls,FPL RVôôõl× ÏÝ Eßl©]ôóLs B¡úVôÚdÏ G]Õ U]UôôókR TôWôhÓRpLû[EôõjRôdÏ¡ú\u.
CWôú_x ALoYôp, I. A. S.,ùTôÕ CVdÏSo / CûQ ùNVXô[o
§\u úUmTôÓ Utßm ùRô¯p
Øû]úYôôó AûUfNLm
Ck§V AWÑ
×Õ ¥p≠ þ 110 001.
© NIMI, Not to be republished
(iv)
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Ck§V AW£u ùRô¯Xô[ôó Utßm úYûXYônl× AûUfNLj§u ̧ Ýs[ úYûX Yônl× UtßmùRô¯tT«t£j Õû\«u ùTôÕ CVdLLjRôp (D.G.E&T) (RtùTôÝÕ T«t£jÕû\ CVdLLj§u¸Ýs[ §\u úUmTôÓ Utßm ùRô¯p Øû]úYôo AûUfNLm, ù_ôóU² áh¥ûQl× Ï¥VWÑùRô¯p ÖhT ER®ÙPu úR£V ùRô¯tT«t£ FPL RVôôõl× ¨ûXVm(NIMI) ùNuû]«p 1986p ÕYdLlThPÕ. Ck¨ûXVj§u Ød¡V ϱdúLôs TpúYß ùRô¯t©ôõÜLÞdÏm, ûL®û]OôóUtßm ùRô¯p T«t£ §hPTôÓLÞdÏ úR£V §\u Rϧ LhPûUl× (NSQF ) YÏjÕûWjRTôPj §hPeL°u T¥ Lt©jRÛdLô] FPLeLû[ EÚYôd¡ AYtû\ YZeÏRp BÏm.
CkR Lt©jRÛdLô] NôR]eLs JÚ LÚj§Vp FPL £lTeLs Y¥®p (IMP) LÚj§Vp ×jRLm,ùNnØû\ ×jRLm, úNôRû] Utßm §\]ônÜ T«t£ (Test & Assignment) ×jRLm, T«tßSôóY¯Lôh¥, úLh£ Lôh£ LÚ® (ÑYôó ®[dLlTPm Utßm Jüõ×Ïm FPLm) B¡VYtû\Es[Pd¡«ÚdÏm. CkR NôR]eLs ùRô¯tT«t£ ¨ûXVj§u (ITI) T«t£«u JhÓ ùUôjRRWj§û] EVojR TVuTÓm.
“§\u Ck§Vô” Guß AûZdLlTÓ¡\ úR£V Tp§\u (multi skill) §hPØuYûWÜ (programes),Ck§V AW£u ̈ § AûUfNLj§u (ùTôÚ[ôRôW ©¬Ü)þu ̧ r 27þ12þ2013 úR§«hP AWNôûQ«uYô«XôL ùY°«PlThPÕ. CRu êXm §\u úUmTôh¥u ¸r Ck§V Cû[OoLÞdÏ A±ÜUtßm §\ûUûV A§L¬dL Y¯YûL ùNnÕ ARu êXm קV Yônl×Lû[ EÚYôdLÜm§hPªPlThPÕ.
CRu Ød¡VjÕYm Ck§V Cû[OoL°u §\û] úUmTÓj§ ARuêXm AYoLs úYûXYônl× ùT\Üm, úUÛm ùRô¯p Øû]úYôo T«t£ A°jRp êXm, AYoLs ÑV ùRô¯p ׬VBRWÜ Utßm Y¯LôhÓRp êXm Sm TôWmT¬V ùRô¯ûXÙm £\lTôL ùNnV Ø¥Ùm. CkRT«t£Ls NoYúRN RWj§u A¥lTûP«p CÚlTRôp, Sm Sôh¥u Cû[OoLs Ck§VA[®ÛmUtßm AVpSôh¥Ûm T¦×¬VÜm Y¯ YûL HtTÓm. CkR “úR£V §\u RϧLhPûUl×” (NSQF) úR£V §\u úUmTôhÓ ØLûU (NSDA) Guß AûZdLlTÓ¡\AûUl©]Wôp C§p GpXô®RUô] RϧLû[Ùm JÚ ùRôPof£Vô] A±Ü ¨ûX, §\u,GiQm úUmTôÓ B¡VYtû\ AûPV Ø¥Ùm. CkR NSQF þu ¸r T«t£Vô[o GkR¨ûXdLô]Rϧ ¨ûXûVÙm úSW¥ T«t£ êXúUô ApXÕ Uû\ØL T«t£ êXúUô ApXÕ AàTYT«t£«u êXUôLúYô AûPV Ø¥Ùm.
CkR T¦Uû] LQdÏ Utßm A±®Vp (Aû]jÕ ùTô±«Vp ©¬ÜLÞdÏm ùTôÕYô]Õ)×jRLUô]Õ Ød¡V ÏÝ Eßl©]oL[ôp NSQF TôPj§hPj§u ¸r EÚYôdLlThPÕ.
CkR T¦Uû] LQdÏ Utßm A±®Vp NSQF TôPj§hPj§u T¥ (Aû]jÕ ùTô±«Vp©¬ÜLÞdÏm ùTôÕYô]Õ) ØRp TÚY ×jRLm Ød¡V ÏÝ Eßl©]oL°u áhÓ ØVt£VôÛm(C§p Lp®Vô[o/ ùRô¯p Øû\ Lp® ¨ßY]eL[ô] (IIT) Utßm TX) Utßm (DGE&T) þu ¸rCVeÏm ùRô¯t T«t£ ¨ûXVeL°p T¦ ׬Ùm AYWYo ùRô¯p Õû\«p §\]ôLEs[YoLs, Utßm (MDC) Eßl©]oLs Utßm (NIMI) F¯VoLs B¡úVôoL[ôpEÚYôdLlThPRôÏm. úUúX á\lThP ×jRLm, T«tß®lTYo Utßm T«t£Vô[¬u ¿iPSôû[V ®ÚlTUô] ùRô¯p NôokR Õû\«p T«t£ ùLôÓjÕ úYûX Yônl©û] A§L¬dÏm®RUôL ØÝûUVôL §Úl§ A°dÏm G] Sm©dûL ùR¬®jÕ (NIMI) YôrjÕ¡\Õ.
CfNkRolTj§p (NIMI), GpXô Eßl©]oLÞdÏm Utßm FPL RVô¬l× ÏÝ Eßl©]oLÞdÏmR]Õ EiûUVô] Su±«û] ùR¬®jÕd ùLôs¡\Õ.
Bo. ©. §eWôùNuû] - 600 032 ùNVp CVdÏSo, NIMI
© NIMI, Not to be republished
(v)
HtT±®l×
NSQF TôPj§hPj§uT¥ (ØRp TÚYm) “T¦Uû] LQdÏ Utßm A±®Vp” (Aû]jÕùTô±«Vp ©¬ÜLÞdÏm ùTôÕYô]Õ) ùRô¯tT«t£ FPL £lTeLû[ (IMP)ùY°dùLôQW LôWQUô] ¸rLiP FPL RVô¬l× Eßl©]oL°u JjÕûZl× Utßm
AYoL°u TeL°l©tÏ úR£V ùRô¯tT«t£ FPL RVô¬l× ¨ûXVm (NIMI) R]Õ
Su±«û] ùR¬®jÕd ùLôs¡\Õ.
FPL úUmTôh¥u JÚe¡ûQlTô[oLs
§Ú. K. º²YôN Wôq - CûQ CVdÏSo,
UiPX ùUô¯ ùTVol× ùTôßlTô[o,
NIMI, ùNuû].
§Ú. G . ûUd¡s _ô² - T«t£ AÛYXo,
JÚe¡ûQlTô[o NIMI,ùNuû].
RªZôdLm
§Ú. C.C . Ñl©WU¦Vu - T«t£ A§Lô¬, (KnÜ)
TôX Uk§o PHMITI,ùNuû] þ 600017
§Ú. G . ù_VWôUu - ER® T«t£ AÛYXo, (KnÜ)
AW£]o ùRô¯tT«t£ ¨ûXVm,
AmTjço, ùNuû] þ 600058
CkR £lTjûR (IMP) EÚYôdÏm ùNVtTôh¥p ªLÜm £\lTôLÜm BrkR DÓTôÓPàmT¦Vôt±V L¦² RhPfNo, L¦² YûW LûXOo ªûN AfÑl T§lTô[o B¡úVôÚdÏ
úR£V ùRô¯tT«t£ FPL RVôôõl× ¨ûXVm (NIMI) R]Õ TôWôhÓRûXl T§Ü ùNn¡\Õ.
CkR ×jRLjûR EÚYôdLl TeL°l× Sp¡V CRW T¦Vô[oL°u ØVt£LÞdÏm úR£V
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© NIMI, Not to be republished
(vi)
A±ØLm
Cl×jRLm ÑVUôL LtTRtÏ Ht\ AXÏL[ôL ©ôõdLlThÓs[Õ. JqùYôÚ RûXl©tÏm Ht\ûRÑÚdLUôL §Wh¥ ùLôÓdLlThÓs[Õ Utßm §\]ônÜ T«t£ TϧÙm Es[Pe¡VÕ.ùR°YôLÜm, ÑXTUôLÜm ×ôõkÕùLôs[dá¥V Øû\«p T¦Uû] LQdÏLs Utßm A±®VpA¥lTûP RjÕYeLs ÑÚdLUôL ®YôõdLlThÓs[Õ. YÏl× Aû\«p T«t£Vô[oLÞdÏT«tß]ôó A°dÏm ®[dL EûWdÏ CûR JÚ Uôt\ôLd LÚRdáPôÕ. ¨fNVUôL CÕ ªLÜm®ôõYô]RôL CÚdÏm. Cl×jRLj§u êXm T«t£Vô[oLs úRûYVô]ûYLû[ ùT\ Ø¥Ùm.T«tß]o êXm ®ôõYôL ùRôõkÕ ùLôs[Xôm Utßm AkRkR Tϧ«p Es[ §\]ônÜT«t£Lû[ ÑVUôL ¾oÜ LôQXôm. TXYûLVô] LQdÏLû[ Cl×jRLj§u ER®Vôp ¾oÜLôQXôm. T¦Uû]«p ùNnØû\ T«t£«u ùTôÝÕ HtTPdá¥V NkúRLeLÞdÏ CÕ ªLÜmER®VôL CÚdÏm.
§\]ônÜ T«t£, YûWLûX (graphics) êXUôL ùLôÓdLlThÓs[Rôp T«t£Vô[o G°RôL׬kÕ ùLôs[ Ø¥Ùm. úUÛm LQdÏLû[ ¾oÜ LôiTRtÏ N¬Vô] Y¯Øû\Lû[ CRuêXm T«t£Vô[oA±VXôm. LQdÏLû[ ¾oÜ ùNnYRtÏj úRûYVô] ϱl×Ls (data)YûWLûXdÏ AÚ¡p ϱÂÓLs (A) YôojûRLs êXm ùLôÓdLlThÓs[Õ. LQdÏL°pϱdLlThP ϱÂÓLs HtL]úY ARtÏj ùRôPo×ûPV RûXl×f ÑÚdLj§p Es[Õ
JqùYôÚ T«t£«u Ø¥®Ûm GeÏ úRûYúVô AeÏ ARtÏj úRûYVô] §\]ônÜ T«t£Ls,
LQdÏLs úUÛm T«t£dLôL ùLôÓdLlThÓs[].
JÕdLlThP úSWm:
ØRp TÚYj§tLô] LôX AYLôNm (26 YôWeLs) : 52 U¦ úSWm
¡ûPdLlùTt\ TVàs[ YôWeLs (22 YôWeLs) : 44 U¦ úSWm
§Úl×Rp Utßm úRoÜLs (4 YôWeLs) : 8 U¦ úSWm
JÕdLlThP ùUôjR úSWm : 52 U¦ úSWm
JqùYôÚ TϧdÏm JÕdLlThP LôX A[ÜLs ¸úZ ùLôÓdLlThÓs[]. T«tß]oLs CkRLôX AYLôNj§û] TVuTÓj§d ùLôsÞUôß úLhÓd ùLôs[lTÓ¡\ôoLs.
Y.Gi Tϧ T«t£ Gi JÕdLlThP úSWm (U¦«p)
1 AXÏ Øû\Ls, LôW¦Ls Utßm 1.1.01 - 1.2.09 10 U¦ úSWm©u]eLs
2 YodL êXm, ®¡Rm Utßm ®¡R 1.3.10 - 1.5.16 12 U¦ úSWmNUm, NRÅRm
3 CVtL¦Rm (ØRp TÚY EúXôLj 1.6.17 - 1.6.18 4 U¦ úSWmRLÓ úYûXVôs (SMW) -dÏ UhÓm)
4 ùTôÚs A±®Vp, ¨û\, GûP 1.7.19 - 1.8.26 14 U¦ úSWmUtßm APoj§
5 úYLm Ut\m §ûN úYLm, úYûX, 1.9.27 - 1.10.30 8 U¦ úSWm§\u Utßm Bt\p
6 ùYlTm Utßm ùYlT¨ûX (ØRp TÚY 1.11.31 - 1.12.37 6 U¦ úSWmMR&AC Utßm EúXôLjRLÓ úYûXVôs(SMW) -dÏ UhÓm)
7 A¥lTûP ªu²Vp (ØRp TÚY 1.13.38 - 1.13.41 9 U¦ úSWmMR&AC -dÏ UhÓm)
© NIMI, Not to be republished
(vii)
ùTôÚ[PdLm
T«t£ Gi T«t£L°u RûXl×Ls TdL Gi
Tϧ 1
1.1.01 AXÏØû\L°u YûLLs (Classification of system of units) 1
1.1.02 A¥lTûP Utßm YûWVßdLlThP AXÏLs F.P.S,C.G.S, M.K.S Utßm SI AXÏLs (Fundamental and Derived unitsF.P.S, C.G.S, M.K.S and SI units) 3
1.1.03 A[ÅhÓ AXÏLs Utßm Uôt\eLs (Measurement unitsand conversion) 6
1.1.04 ¿[m, ¨û\, ®ûN, úYûX, §\u Utßm Bt\ûXUôtßRp (Conversions of length, mass, force,work, power and energy) 14
1.2.05 LôW¦Ls, HCF, LCM Utßm LQdÏLs (Factors, HCF,LCM and problems) 16
1.2.06 ©u]eLs (Fractions) 18
1.2.07 RNU ©u]eLs (Decimal fractions) 21
1.2.08 TôdùLh LôpÏúXhPo Utßm ARu TVuTôÓLs (Pocketcalculator and its applications) 25
1.2.09 LôpÏúXhPûW TVuTÓj§ ¾oÜ LôÔRp (Solving problemsby using calculator) 29
Tϧ 2
1.3.10 YodLm Utßm YodLêXm (Square and square root) 32
1.3.11 LôpÏúXhPûW TVuTÓj§ G°V LQdÏLs ùNnRp(Simple problems using calculator) 33
1.3.12 ©RôLWv úRt\jûR TVuTÓj§ ùNnVlThPLQdÏLs (Applications of pythagoras theorem and related problems) 34
1.4.13 ®¡Rm Utßm ®¡R NUm (Ratio and proportion) 35
1.4.14 úSôó Uô\p Utßm G§ôó Uô\p (Direct and indirect proportions) 37
1.5.15 NRÅRm (Percentage) 42
1.5.16 NRÅRj§≠ÚkÕ RNU©u]m Utßm NôRôWQ ©u]UôLUôtßRp (Changing percentage to decimal and fraction) 46
Tϧ 3 (ØRp TÚY EúXôLjRLÓ úYûXVôs(SMW) -dÏ UhÓm)
1.6.17 CVtL¦Rd ϱÂÓLs Utßm A¥lTûPLs(Algebraic symbols and fundamentals) 47
1.6.18 CVtL¦Rj§p Es[ ©¬Yô] áhPp, L¯jRp, ùTÚdLpUtßm YÏjRp (Addition,subtraction,multiplication and divisionof algebra) 51
Tϧ 4
1.7.19 EúXôLeL°u CVt©Vp Utßm CVk§W®Vp RuûULs(Physical and mechanical properties of metals) 54
© NIMI, Not to be republished
(viii)
T«t£ Gi T«t£L°u RûXl×Ls TdL Gi
1.7.20 CÚm× Utßm Yôol× CÚm©tLô] A±ØLm (Introduction ofiron and cast iron) 57
1.7.21 CÚm×fNjÕs[ Utßm CÚm×fNj§pXôR EúXôLYûLLs (Types of ferrous and non ferrous metals) 61
1.7.22 CÚm©tÏm, G@¡tÏm CûPúVVô] ®j§VôNeLs, LXl×G@Ï Utßm LôoTu G@Ï (Difference between iron & steel, alloysteel & carbon steel) 65
1.7.23 CWlTo, UWm Utßm CuÑúXh¥e ùTôÚsLÞdLô]RuûULs Utßm ETúVôLeLs (Properties and uses of rubber,timber and insulating materials) 67
1.8.24 ¨û\, ¨û\«u AXÏLs, APoj§ Utßm GûP (Mass,units of mass, density and weight) 71
1.8.25 ¨û\ Utßm GûPdÏ CûPúVVô] ®j§VôNm, APoj§Utßm APoj§ GiÔdÏ CûPúVVô] ®j§VôNm(Difference between mass & weight, density & specific gravity) 72
1.8.26 ¨û\, GûP Utßm APoj§ B¡VYtßdLô] ùRôPo×LQdÏLÞm §\]ônÜ T«t£LÞm (Related problems withassignment of mass, weight & density) 74
Tϧ 5
1.9.27 KnÜ, CVdLm, úYLm, §ûN úYLm, úYLm Utßm §ûNúYLj§tLô] úYßTôÓ, ØÓdLm Utßm Ïû\ØÓdLm(Rest, motion, speed, velocity, difference between speed & velocity,acceleration & retardation) 81
1.9.28 úYLm Utßm §ûNúYLj§tÏ ùRôPo×ûPVLQdÏLÞm §\]ônÜ T«t£LÞm (Related problems withassignment of speed & velocity) 87
1.10.29 úYûX«u AXÏ, §\u Utßm Bt\p, Cu_÷²uϧûWj§\u Utßm CVk§W XôTm (Units of work, power andenergy, horse power of engines and mechanical efficiency) 91
1.10.30 ¨ûX Bt\p, CVdL Bt\p Utßm AYt±tÏùRôPo×ûPV LQdÏLs Utßm §\]ônÜ T«t£ (Potentialenergy, kinetic energy and related problems with assignment ) 94
Tϧ 6 (ØRp TÚY MR&AC Utßm EúXôLjRLÓúYûXVôs (SMW) -dÏ UhÓm)
1.11.31 ùYlTm Utßm ùYlT¨ûX LÚjÕÚ, ùYlTj§u®û[ÜLs, ùRoúUôÁhPo vúLp, ùNp£Vv, @TôWuaöh, ìUo, ùLp®u Utßm ùYlTm Utßm ùYlT¨ûXdÏCûPúVVô] úYßTôÓLs (Concept of heat and temperature,effects of heat, thermometer scale, celcius, fahrenheit, reaumer, kelvin anddifference between heat and temperature) 97
1.11.32 ùYlT¨ûXLû[ ùNu¥¡úWÓ, @TôWu aöh, ìUo,ùLp®u B¡V vúLpL°p Uôt\m ùNnRp (Conversionbetween centigrade, fahrenheit, reaumer, kelvin scale of temperature) 100
© NIMI, Not to be republished
(ix)
T«t£ Gi T«t£L°u RûXl×Ls TdL Gi
1.11.33 ùYlT¨ûXûV A[dÏm LÚ®Ls, ùYlTUô²«uYûLLLs, ûTúWôÁhPo Utßm ùYlT T¬Uôt\m(Temperature measuring instruments, types of thermometer, pyrometerand transmission of heat ) 101
1.11.34 ¿[l ùTÚdL Gi Utßm ARtÏ ùRôPo×ûPVLQdÏLs Utßm §\]ônÜ T«t£ (Co-efficient of linearexpansion and related problems with assignment) 104
1.11.35 ùYlT CZl× Utßm ùYlT Ht× LQdÏLs Utßm§\]ônÜ T«t£ (Problems of heat loss and heat gain with assignment) 107
1.11.36 AÝjRj§u LÚjÕÚ Utßm TpúYß Øû\L°p ARuAXÏLs (Concept of pressure and its units in different system ) 112
1.12.37 ùYlT LPjÕm §\u Utßm Lôl× ùTôÚsLs (Thermalconductivity and insulations) 113
Tϧ 7 (ØRp TÚY MR&AC -dÏ UhÓm)
1.13.38 A±ØLm, ªuNôWj§u ETúVôLeLs, Uô≠dëp,AÔ, ªuNôWm RVô¬jRp, ªuú]ôhPm, ªu]ÝjRm,ªuRûP Utßm ARu AXÏLs (Introduction, use of electricity,molecule, atom, producing electricity, electric current, voltage, resistanceand their units ) 116
1.13.39 Kªu ®§, LQdÏLs Utßm V.I.R CûP«Xô] E\ÜLs,ùRôPo ªu ÑtßLs Utßm CûQªu ÑtßL°uLQdÏLs (Ohm’s law, relation between V.I.R & problems, series & parallelcircuits problem ) 118
1.13.40 ªuNd§, Bt\p Utßm ARu AXÏLs, §\]ônÜ T«t£Utßm LQdÏLs (Electrical power, energy and their units, calculationwith assignment ) 121
1.13.41 LôkR çiPp, Ru ªu çiPp Utßm TWvTW ªuçiÓ§\u Utßm ªu CVdÏ ®ûN EtTj§ (Magneticinduction, self and mutual inductance and EMF generation ) 127
Lt\≠u ØÝûUûV U§lÀÓ ùNnÙm Øû\ LEARNING / ASSESSABLE OUTCOME
Cl×jRLj§u Ø¥®p ¿eLs §\m ùT\ CÚlTûY
• A¥lTûP ªu²Vp ARu Au\ôP TVuTôÓ, CûRl Tt±VTôPl׬RÛPu TpúYß YûLVô] L¦Rm Utßm A±®VpTVuTôÓLs Utßm AYtû\ G°ûUVôL ׬kÕ ùLôsÞRp[TpúYß YûL L¦Rm Utßm A±®Vp - AXÏLs, LôW¦Ls-Utßm ©u]eLs, YodL êXm, ®¡Rm Utßm ®¡R NUm,NRÅRm, ùTôÚs A±®Vp, ¨û\, GûP, APoj§, úYLmUtßm §ûNúYLm, úYûX, §\u Utßm Bt\p, CVtL¦Rm,ùYlTm Utßm ùYlT¨ûX, ªuNôWj§u A¥lTûP, AÝjRm]
• SMW - CVtL¦Rm Utßm ùYlTm Utßm ùYlT¨ûX
• MR & AC - ùYlTm Utßm ùYlT¨ûX Utßm ªuNôWj§uA¥lTûP
© NIMI, Not to be republished
(x)
SYLLABUSFirst Semester Common for All Engineering Trades Duration: Six Months
(Except MR&AC and SMW)
S.no. Title
Unit
Fractions
Square Root
Square and Square Root, method of finding out square roots, Simple problem using calculator.
Ratio & Proportion
Simple calculation on related problems.
Introduction, Simple calculation. Changing percentage to decimal and fraction and vice-versa.
Percentage
Fractions, Decimal fraction, L.C.M., H.C.F., Multiplication and Division of Fractions and Decimals,conversion of Fraction to Decimal and vice versa. Simple problems using Scientific Calculator.
1
2
3
4
5
Systems of unit- FPS, CGS, MKS/SI unit, unit of Length, Mass and Time, Conversion of units.
Material Science
Properties - Physical & Mechanical, Types - Ferrous & Non-Ferrous, difference between Ferrous andNon-Ferrous metals, introduction of Iron, Cast Iron, Wrought Iron, Steel, difference between Iron andSteel, Alloy steel, Carbon steel, Stainless steel, Non-Ferrous metals, Non-Ferrous Alloys.
6
Mass, Weight and Density
Mass, Unit of Mass, Weight, difference between mass and weight, Density, unit of density, SpecificGravity of metals.
7
Speed and Velocity
Rest and Motion, Speed, Velocity, difference between speed and velocity, Acceleration, Retardation,equations of motions, simple related problems.
8
Work, Power and Energy
Work, unit of work, Power, unit of power, Horse power of engines, Mechanical Efficiency, Energy,use of energy, Potential and Kinetic energy, examples of potential energy and kinetic energy.
9
© NIMI, Not to be republished
(xi)
Mechanic Refrigeration and Air Conditioning
General simplifications
Fractions, Types of fractions, Common fractions, Decimal fractions with examples. Addition,Subtraction, Multiplication and Division of fraction, conversion of Fraction to Decimal and vice versa.
S.no. Title
1
2 Square & Square root
Square root of perfect square, Square of Whole Number and Decimal. Applications of Pythagorastheorem and related Problems.
3 Unit & Measurements
Definition, classification of System of units, Fundamental & Derived units. C.G.S, M.K.S,. F.P.S, & S.ISystem of units. Metric system of weight and measurement unit and conversion factors, problems.
4 Percentage
Introduction, Simple calculation. Changing percentage to fraction and decimal & vice-versa.
5 Introduction, use of Electricity, Molecule, Atom, and How Electricity is Produced, Electric current,Voltage, Resistance and their units. Ohm’s law. Relation between V.I.R & Problems. Series & Parallelcircuits & Problems. Electrical Power and energy & their units & calculation.
6 Magnetic Induction, Self & Mutual Inductance, EMF generation.
7 Material Science
Properties of metals - Physical & Mechanical, Meaning of Tenacity, Elasticity, Malleability, Brittleness,Hardness, Ductility. Types – Ferrous & Non-Ferrous, difference between Ferrous and Non-Ferrousmetals, introduction of Iron, Cast Iron, Wrought Iron, Steel, difference between Iron and Steel, Alloysteel, Carbon steel, Stainless steel, Non-Ferrous Alloys. Effect of Alloying elements.
8 Properties and uses of Copper, Zinc, Lead, Tin, Aluminium etc., Properties and uses of Brass,Bronze as bearing material.
9 Heat and Temperature
Measurement of Temperature, Boiling and Melting points. Interchange of heat, (Principle ofcalorimetry) Co-efficient of linear expansion, Related problems.
10 Vapours and gases
Saturated and superheated vapours, Critical pressures and temperatures. Heat transfer -Conduction, Convection, Radiation. Thermal conductivity and Insulations.
Syllabus for Mechanic Refrigeration & Air Conditioning
© NIMI, Not to be republished
(xii)
Sheet Metal Worker
Introduction and Importance of Science and Calculation to the Trade skill.
S.no. Title
1
2 - System of Units: British, Metric and S. I. Units for Length, Mass, Area, Volume, Capacity andTime.
- Conversions between British and Metric Systems.
3 - Density & Specific gravity.
- Mass, Weight. Definition and units.
4 - Metals: Properties and uses of Cast iron, Wrought iron, Plain carbon steels and Alloy steels.
- Difference between metals, non-metals and alloys.
5 Properties and uses of Copper, Zinc, Lead, Tin and Aluminium.
6 Properties and uses of Brass, Bronze, Rubber ,Timber and Insulating materials.
7 Concept of Heat and Temperature. Difference between heat and temperature. Effects of Heat,Thermometer Scales such as Celcius, Fahrenheit and Kelvin, Temperature measuring Instruments -types of thermometers and pyrometers.
8 - Conversions between the above Scales of Temperature.
- Units of Heat-Calorie, B.Th.U & C.H.U., Joule.
- Concept of Specific Heat, Latent Heat, problems on Heat Loss and Heat Gain.
9 - Definition of Force: Units of Force in M.K.S.& S.I. Systems.
- Concept of Pressure and its Units in different systems.
10 - General simplifications: BODMAS rule.
- Fraction: Addition, Subtraction, Multiplication and Division-Problems.
- Decimal: Addition, Subtraction, Multiplication, and Division-Problems.
11 Conversion of Fraction to Decimal and vice-versa.
12 Square roots: The Square and Square root of a Whole Number and Decimal.
13 Percentage: Changing Percent to Decimal and Fraction and vice versa, applied problem.
14 Concept on Ratio and Proportion-Direct and Inverse Proportion, simple applied problems.
15 Algebraic Symbols and Fundamentals - Addition, Subtraction, Multiplication and Division-Problems.
Syllabus for Sheet Metal Worker
© NIMI, Not to be republished
(xiii)
Title of the Contents Common for all MR&AC SMWEngineering Trades
1 Unit
2 Fraction
3 Square root
4 Ratio & Proportion ⎯
5 Percentage
6 Algebra ⎯ ⎯
7 Material Science
8 Mass, Weight & Density ⎯
9 Speed & Velocity ⎯ ⎯
10 Work, Power & Energy ⎯ ⎯
11 Heat & Temperature ⎯
12 Basic Electricity ⎯ ⎯
Summary of Contents
© NIMI, Not to be republished
© NIMI, Not to be republished
1
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© NIMI, Not to be republished
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6
A[ÅhÓ AXÏLs Utßm Uôt\eLs T«t£ 1.1.03
AXÏLÞm ÑÚdLeLÞm
A[ÜLs AXÏLs AX¡uÑÚdLm
LúXôôõ©d úYpë ¡úXô _øp/¡úXô ¡Wôm kJ/kg
ϱl©hP G¬lùTôÚs ¡úXô ¡Wôm/U¦dÏ/¨ëhPu kg/hr/N
¿[m ª.ÁhPoLs, ÁhPoLs mm, m, km¡úXô ÁhPoLs
¨û\ ¡úXô¡Wôm, ¡Wôm kg, g
úSWm ®]ô¥Ls, ¨ªPeLs, U¦Ls s, min, h
úYLm ùNu¥ÁhPôó/®]ô¥Ls cm/s, m/sÁhPo/®]ô¥Ls¡úXôÁhPôó/U¦dÏ ,ûUp/U¦dÏ km/h, mph
ØÓdLm ÁhPôó/NÕW ®]ô¥ m/s2
®ûN ¨ëhPuLs, ¡úXô¨ëhPuLs N,kN
ØùUih ¨ëhPuþÁhPôóv Nm
úYûX _÷pv J
§\u ϧûWj§\u,Yôhv,¡úXôYôhv Hp, W, kW
AÝjRm ¨ëhPuv/NÕW ÁhPôó N/m2
¡úXô ̈ ëhPuv/NÕW ÁhPôó kN/m2
úLôQm úW¥Vu rad
úLôQ úYLm úW¥Vu/®]ô¥ rad/s
úW¥Vu/NÕW ®]ô¥ rad/s2
JÚ ¨ªPj§p Ñtßm Ñtß RpmJÚ ®]ô¥«p Ñtßm Ñtß rev/s
ùP£Up TYo U§l× ©¬©dv ϱÂÓ ®[dLm
ùP£U≠u UPeÏLs Utßm AX¡u TôLeLs (Decimal multiples and parts of unit)
1012 1000000000000 ùPWô T ©p≠Vu UPeÏ
109 1000000000 _õLô G B«Wm ªp≠Vu UPeÏ
106 1000000 ùULô M ªp≠Vu UPeÏ
103 1000 ¡úXô K B«Wm UPeÏ
102 100 ùadúPô h èß UPeÏ
101 10,101 ùPLô da TjÕ UPeÏ
10-1 0.1, 10-1 ùP£ d Tj§p JÚ TeÏ
10-2 0.01 ùNu¥ c è±p JÚ TeÏ
10-3 0.001 ªp≠ m B«Wj§p JÚ TeÏ
10-6 0.000001 ûUdúWô μ ªp≠V²p JÚ TeÏ
10-9 0.000000001 SôúSô n B«Wm ªp≠V²p JÚ TeÏ
10-12 0.000000000001 ©úLô p ©p≠V²p JÚ TeÏ
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7
A[ÜLs SI AXÏ →→→→→©ôõh¥x AXÏ ©ôõh¥x AXÏ →→→→→ SI AXÏ
¿[m 1 Á = 3.281 A¥ 1 A¥ = 0.3048 Á
1 ¡.Á = 0.621 ûUp 1 ûUp = 1.609 ¡.Á
úYLm 1 Á/ùNLuh = 3.281 A¥/ùNLuh 1 A¥/ùNLuh = 0.305 Á/ùNLuh
1 km/h = 0.621 mph 1 mph = 1.61 km/h
ØÓdLm 1 Á/ùNLuh2 = 3.281 A¥/ùNLuh2 1 A¥/ùNLuh2 = 0.305 Á/ùNLuh2
¨û\ 1 ¡úXô = 2.205 TÜih 1 TÜih A¥ = 0.454 ¡úXô
®ûN 1 ¨ëhPu = 0.225 TÜih A¥ 1 TÜih A¥ = 4.448 ¨ëhPu
(1 MN = 1 ùULô ¨ëhPu = 1 ªp≠Vu ̈ ëhPu)
Pôôód 1 ¨ëhPu Á= 0.738 TÜih 1 TÜih A¥/A¥= 1.355 ̈ ëhPuA¥/A¥ ÁhPôó
AÝjRm 1 ̈ ëhPu/ÁhPôó2 = 0.000145 1 TÜih A¥/AeÏXm2
TÜih A¥/AeÏXm2 = 6.896 ¡úXô ¨ëhPu/ÁhPôó2
1 Pa = 1 ¨ëhPu/ÁhPôó2
1 Tôôó = 14.5038 TÜih 1 TÜih A¥/AeÏXm2 = 6.895 ¡úXôA¥/AeÏXm2 ̈ ëhPu/ÁhPôó2
Bt\p, úYûX 1 J = 0.738 A¥ TÜih A¥ 1 A¥ TÜih A¥ = 1.3558 J1 J = 0.239 LúXôôõ 1 LúXôôõ = 4.186 J1 kJ = 0.948 Btu 1 Btu = 1.055 kJ
(1 therm = 100 000 Btu)1 kJ = 0.526 CHU 1 CHU = 1.9 kJ
§\u 1 ¡úXô Yôhv = 1.34 ϧûW §\u 1 ϧûW §\u = 0.7457 ¡úXô Yôhv
GôõùTôÚs 1km/L = 2.82 ûUp/úLXu 1 ûUp/úLXu = 0.354 km/LTVuTôÓ
ϱl©hP 1 kg/kWh = 1.65 lb/bhp h 1 lb/bhp h = 0.606 kg/kWhGôõùTôÚs 1 litre/kWh=1.575 pt/bhp h 1 pt/bhp h = 0.631 litre/kWhTVuTôÓ
LúXôôõ©d 1 kJ/kg = 0.43 Btu/lb 1 Btu/lb = 2.326 kJ/kgúYpë 1 kJ/kg = 0.239 CHU/lb 1 CHU/lb = 4.188 kJ/kg
NoYúRN Øû\ AXÏLs Utßm ©ôõh¥x AXÏLs (SI units and the British units)
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.1.03
© NIMI, Not to be republished
8
Nm2
Nm2
M
ùYlT Bt\pùYlT A[Ü
AÝjRm P ¨ëhPu/ÁhPôó2
¨ëhPu/ÁhPôóó2
YûWVû\ÙPu AXÏLû[ A[dL TZÏRp (Units in measuring practice with definitions)
A[ÜLs AXÏ ®[dLm
N 1 ¡úXô ¨û\Ùs[ JÚ ùTôÚ°uÁÕ ùNVpThÓ 1m/s2 ØÓdLjûRHtTÓjÕm ®ûN 1 ¨ëhPuBÏm.JÚ ùTôÚ°u ¨û\1 ¡úXô1 ̈ ëhPu = 1 ¡úXô ÁhPôó/ùNLih2
1 ̈ ëhPu/ÁhPôó2 (1 pascal)AÝjRj§tÏ NUUô]Õ. ARôYÕ1 ̈ ëhPu ®ûN JÚ NÕW ÁhPôóTWl©tÏ ùNeÏjRôLl ùNVpTÓ¡\Õ.
TôvLp Pa 1 Pa = 1 ¨ëhPu/ÁhPo2 1 Tôo (1bar)GuTÕ 100 000 Pa dLô] £\l× ùTVoBÏm.
1 ̈ ëhPu/ÁhPôó2 (1 TôvLp)ùUdLô²dLp v¥Wv RûLÜ,1 ̈ ëhPu RûLYôL JÚ NÕWÁhPoTWl©u ÁÕ ùNVpTÓjRlTÓ¡\Õ.ùTô±«V≠p TX ©¬ÜL°p CkRCVk§W RûLÜ Utßm Eߧ¨ëhPu/ ÁhP¬p ϱdLlTÓ¡\Õ.1 ̈ ëhPu/ÁhPôó2 = 1000 000 TôvLp= 1 MPa®ûN«u §ûN«p 1 N ®ûNûVTVuTÓj§ AkR §ûN«p 1 ÁSLojÕm úYûX«u A[Ü 1 _÷p -dÏ NUm.1 _÷p = 1 ¨ëhPu Á = 1 Ws = 1 kgm2/s2
3600 000 _÷p = 1 ¡úXô Yôhv AYôó
Nm 1 ̈ ëhPu úUôùUuh BlúTôôóÑdÏ NUUô]Õ.
J CÕ JÚ ¨ëhPu Utßm 1 ÁhPôóùSm×úLôp×Vj§u ùTÚdÏjùRôûLVôÏm. 1 ¨ëhPu ÁhPôó = 1_øp = 1 Ws = 1 ¡úXô¡Wôm ÁhPôó2/®]ô¥2
W 1 ®]ô¥ úSWj§p 1 _øp Bt\pUôtßYRtÏj úRûYVô] NU A[ܧ\ú] 1 Yôh G]lTÓ¡\Õ.ªu§\àdLô] ®YWdϱl×LsúYôph Bm©Vo Guß YôhAX¡tÏ T§XôL AûZdLlTÓ¡\Õ.
ùYlT KhPm ø 1 W = 1 J/s = 1 Nm s = 1 VA
NôRôWQ RûLÜCÝj RûLÜ (A)CßdLj RûLÜ,ùYhÓjRûLÜ
®ûN F ¨ëhPu
W _÷p J
¨ëhPuÁhPo_øp
úUôùUihBl úTôôóv
(Pôod)
P Yôh§\uBt\pJhPm
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.1.03
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9
_øp 1 ¡úXô ¨û\ûV ØÝûUVôL/¡úXô¡Wôm GôõjÕ ùY°lTÓjÕm 1 _øp Bt\p
1 _øp/¡úXô¡WôØdÏ NUUô]ùYlTUôÏm.
1 kwh úYûXdÏj úRûYVô]/ ¡WômGôõùTôÚs 1 ¡Wôm /¡úXôYôhU¦dÏf NUUôÏm
ùYlT ¨ûX T ùLp®u K êuß ×s° Ri½ôõuùRôóúUôûP]ªd ùYlTSõûX«u 273 þ 16 Cp JÚ TeÏRôu ùLp®uG]lTÓm.
ªuú]ôhPm I Bm©Vôó A JÚ Bm©Vôó ªuNôWm GuTÕCWiÓ CûQVô] LPj§LÞdÏCûPúV Es[ çWm JÚ ÁhPôõpGXdhúWôûP]ªd ®ûNûV 0.2.10¨ëhPu /JÚ ÁhPôó ¿[j§tÏùLôiÓ YÚYRôÏm.
V úYôph V ùUhPô≠d LiPdPôõu CWiÓ×s°LÞdÏ CûPúV,1 W Nd§ êXmLWih¥u TXm 1 A BÏm. C§p 1Kph GuTÕ GXd¥ôõdúYôpúP_õdÏ NUm BÏm.
R Ohm Ω ùUhPô≠d LiPdPôõu CWiÓ×s°LÞdÏ CûPúV 1Aªuú]ôhPm, 1 V ªu]ÝjRj§pùNpÛm ùTôÝÕ HtTÓm 1 KmªuNôW ªuRûPdÏf NUm.
G ºùUuv S JÚ ºùUuv GuTÕ JÚ KmLiPdPôõu GXd¥ôõd ùW£vPuvÑdÏ NUUô]Õ.
Q áÛml C 1 áÛml GuTÕ GXdhôõ£h¥«uBm©Vôó ®]ô¥ AS A[Ü, ARu KhPm, LPj§«u
ÏßdÏ ùYhÓlTWl©p1s þp ,1AªuNôW ªuú]ôhPUôÏm.
H/μ
gkwh P
Jkg
ùYlT GiûQU§l©ÓRp
GôõùTôÚsTVuTôÓ
ªuNôW ªu]ÝjRm
ªuNôW ªuRûP
ªuNôW LiPdPuv
ªuNôWj§u A[Ü
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.1.03
¡Wôm/ ¡úXôYôh
U¦
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10
RNU ùTÚdLp Utßm UßT¥ÙmùTÚdÏYRtÏ Øu× Es[ûY (Prefixes fordecimal multiples and submultiples)
1 ùULôTôvLp = 1 MPa = 1000000 TôvLp
1 ¡úXôYôh = 1 kW = 1000 Yôhv
1 ùadúPô≠hPôó= 1 hL = 100 ≠hPo
ùPdLô ̈ ëhPu = 1 daN = 10 ̈ ëhPu
ùP£ ÁhPôó = 1 dm = 0.1 ÁhPo
1 ùNu¥ÁhPôó = 1 cm = 0.01 ÁhPo
1 ªp≠ÁhPôó = 1 mm = 0.001 ÁhPo
1 ûUdúWôÁhPôó = 1 um = 0.000001 ÁhPo
ETúVôLm
UôtßYRtLô] LôW¦Ls (Conversion factors)
1 AeÏXm = 25.4 ª.Á
1 ª.Á = 0.03937 AeÏXm
1 ÁhPôó = 39.37 AeÏXm
1 ûUdWôu = 0.00003937AeÏXm
1 ¡úXôÁhPôó = 0.621 ûUpLs
1 TÜih = 453.6 ¡Wôm
1 ¡úXô = 2.205 TÜiÓLs
1 ùUhôõdPu = 0.98 Pu
TWl©uAXÏ (Units of area)
CVt©Vp A[ÜL°u AXÏ (Units ofphysical quantities)
¿[j§u AXÏ (Units of length)
NÕW ªp≠ ÁhPo 1 mm2
NÕW ùNu¥ ÁhPo 1 cm2 = 100 ª.Á2
NÕW ùP£ ÁhPo 1 dm2 = 100 ùN.Á2
NÕW ÁhPo 1 m2 = 100 ùP.Á2
Ho (Are) 1 a = 100 Á2
ùadúPo 1 ha = 100 Ho(a)
NÕW ¡úXôÁhPo 1 km2 = 100 ùadúPo
NÕW AeÏXm 1 sq.in = 6.45 ùN.Á2
NÕW A¥ 1 sq.ft = 0.093 Á2
NÕW L_m 1 sq.yd = 0.84 Á2
NÕW ÁhPo 1 m2 = 10.76 A¥2
HdLo 1 = 40.5 Ho
1 HdLo = 100 ùNuh
1 ùNuh = 436 N.A¥
1 ¡WÜih = 2400 N.A¥
ûUdWôu 1 μ = 0.001 ª.Á
ªp≠ ÁhPôó 1 mm = 1000 μ
ùNu¥ ÁhPôó 1 cm = 10 ª.Á
ùP£ ÁhPôó 1 dm = 10 ùN.Á
ÁhPôó 1 m = 10 ùP.Á
¡úXô ÁhPôó 1 km = 1000 Á
AeÏXm 1" = 25.4 ª.Á
A¥ 1" = 0.305 Á
ùL_m 1 Yd = 0.914 Á
Sôh¥Lp ûUp 1 NM = 1852 Á
_õúVô¡Wôl©dLp 1 = 1855.4 ÁûUp
1 ùadPo = 2.47 HdLo
1 HdLo = 0.4047 ùadPo
1 ùadPo = 10000 N.ÁhPo
GûP«u AXÏ (Units of weight)
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.1.03
úSWm (Time)ùNLih (®]ô¥) 1 S
¨ªPm 1 ¨ªPm = 60 ®]ô¥
U¦ 1 U¦ = 60 ¨ªPm
ªp≠ ¡Wômþ®ûN 1 mgf¡Wômþ®ûN 1 gf 1000 mgf¡úXô ¡Wômþ®ûN 1 kgf = 1000 gfPu 1 t = 1000 kgfAÜuv 1 = 28.35 gfTÜih 1 lbs = 0.454 kgf¿iP Pu 1 = 1016 kgfÏß¡V Pu 1 = 907 kgf
© NIMI, Not to be republished
11
L] A[Ü Utßm ØLjRp A[ÜL°uAXÏLs (Units of volume and capacity)
L] ªp≠ ÁhPôó mm3
L] ùNu¥ ÁhPôó 1 cm3 = 1000 ª.Á3
L] ùP£ ÁhPôó 1 dm3 = 1000 ùP.Á3
L] ÁhPôó 1 m3 = 1000 ùP.Á3
≠hPôó 1 l = 1 ùP.Á3
ùadúPô ≠hPôó 1 hl = 100 ≠hPo
L] AeÏXm 1 cu. in = 16.387 ùN.Á3
L] A¥ 1 cu. ft = 28317 ùN.Á3
úLXu (©ôõh¥x) 1 gal = 4.54 ≠hPo
1L] ÁhPôó 1 m3 = 1000 ≠hPo
1000 L] ùN.Á 1000 cm3 = 1 ≠hPo
1 L] A¥ 1 ft3 = 6.25 úLXu
1 ≠hPôó 1It = 0.22 úLXu
úLôQm (Angle)
1 ùNu¥v£Up AXÏ
1 ùNeúLôQm = 100 ¡úWÓ (100g)
1 ¥¡ôõ (1g) = 100 ̈ ªPm (100’)
1 ¨ªPm (1’) = 100 ùNLuh (100”)
2 ùNdNô_õUp AXÏ
1 ùNeúLôQm = 90 ¥¡¬ (900)
1 ¥¡¬ (10) = 60 ̈ ªPm (60’)
1 ¨ªPm (1’) = 60 ®]ô¥ (60”)
1800
π
π 180
3 YhP AXÏ
úW¥Vu
úW¥VàdÏm Utßm ¥¡¬dÏm CûPúVEs[ E\ÜLs
1 úW¥Vu =
1800 = π úW¥Vu;
1 ¥¡¬ = úW¥Vu
úYûX (Work)
¡úXô¡Wôm-®ûN 1 kgfm = 9.80665 J
ÁhPo 1 kgfm = 9.80665 Ws
_øp 1 J = 1 Nm
Yôh- ùNLih 1 Ws = 0.102 kgfm
¡úXôYôh aYo 1 kWh = 3.6 x 106 J= 859.8845 kcalIT
I.T.¡úXô LúXô¬ 1 kcalIT = 426.kgfm
§\u (Power)
¡úXô¡Wôm ®ûN ÁhPôó/®]ô¥
1 kgfm/s = 9.80665 W¡úXô Yôh 1 ¡úXô Yôh =
1000 Yôh = 1000 J/s
= 102 kgfm/s (úRôWôVUôL)
ùUh¬d ϧûW 1 ϧûW §\u = 75 kgfm/s
§\u = 0.736 kW
1 LúXô¬ = 4.187J
I.T.¡úXô LúXô¬ / aYo
= 1 ¡úXô LúXô¬IT/h
= 1.163 Yôhv
101325 760
TôvLp 1 TôvLp = 1 ̈ ëhPu/ÁhPo2 1 atm = 101325 TôvLp
Tôo 1 Tôo = 10 ¨ëhPu/ùNÁ2 = 100000 Pa–Torr 1 torr =
AhUôv©Vo 1 atm = 1 kgf/cm2 1 kgf/cm2 = 735.6 ª.Á ùUoϬ
AÝjRm (Pressure)
= 133.32 pa
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.1.03
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12
l ¿[m m ÁhPo mh EVWm m ÁhPo mb ALXm m ÁhPo mr BWm m ÁhPo md ®hPm m ÁhPo md,δ ÑY¬u R¥Uu m ÁhPo mS Y¯«u ¿[m m ÁhPo mA (S) TWlT[Ü m2 NÕW ÁhPo m2
V (v) L] A[Ü m3 L] ÁhPo m3
α,β,γ etc úLôQm ° úW¥Vu (1 rad = 57.30) radλ AûX ¿[m km ¡úXôÁhPo kml,la ùNLih úUôùUuh cm4 Metre to the fourthpower m4
Bl H¬Vô
NoYúRNAXÏLsNoYúRNAXÏ
ϱÂÓLs
CVt©VpA[ÜLs
YZdLUô]ϱÂÓLs
ϱÂÓ
_õúVôª§ A[ÜLs (Geometrical quantities)
m ¨û\ kg kg ¡úXô ¡Wôm kgc,ρ APoj§ g/cm3 ¡úXô ¡Wôm/L] ÁhPo ókg/m3
l,J úUôùUuh Bl C]o£Vô kg, m2 ¨ëhPu ÁhPôó Nm
¨û\ (Mass)
T úSWm (A) úSW CûPùY° s ®]ô¥ snu ùWôhúPN]p AûXY¬ûN l/min ùW£lúWôdLp ®]ô¥ l/su,v,w,c §ûN úYLm m/min ÁhPo/®]ô¥ m/sω úLôQ §ûN úYLm rad/s úW¥Vu/®]ô¥ rad/sg Free fall ØÓdLm m/s2 ÁhPo/®]ô¥2 m/s2
a ØÓdLm m/s2 ÁhPo/®]ô¥2 m/s2
Ïû\ ØÓdLm m/s2 ÁhPo/®]ô¥2 m/s2
F ®ûN kgf ¨ëhPu (1kgf = 9.80665N) N
G(P,W) GûP kgf ¨ëhPu N
γ ϱl©hP GûP kgf/m3 ¨ëhPu/L] ÁhPo N/m3
M CVdL ®ûN
(®ûN x çWm) kgf.m ¨ëhPu ÁhPo N.m
P AÝjRm (®ûN/TWlT[Ü) kgf/cm2 TôvLp, ¨ëhPu/N.Á Pa,N/m2
p NôRôWQ RûLÜ kgf/mm2 Tôo (1Tôo=10N/m)
τ p ùYhÓ RûLÜ kgf/mm2 Tôo
E Áh£«Vp ÏQLm kgf/mm2 ¨ëhPu/N.Á N/m2
G ùYhÓ ÏQLm kgf/mm2 ¨ëhPu/N.Á N/m2
μ (f) EWôn®u ùTÚdL ÏQm No Unit
úSWm (Time)
®ûN Utßm AÝjRm (Force and Pressure)
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.1.03
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13
ùNu¥ ¡úWÓ (0C) 00C 1000CúTWuÍh (0F) 320F 2120F
ùLp®u (K) 273K 373KÃUo (0R) 00R 800R
ùYlT ¨ûX (Temperature)
vúLp Eû\ ¨ûX ùLô§ ¨ûX
°R 80
°C100= = = K- 273
100 °F- 32 180
A,W úYûX kgfm _øp (1 _øp=1 ¨ëhPu.Á) J (Nm)
P §\u kgfm/s Yôh W (J/s)
E,W Bt\p kgfm _øp J (Nm)
η TV]ß §\u - - -
W,A,E,Q ùYlT A[Ü kcal _øp J
ùYlTm, úYûX, Bt\p, ®ûN (Heat, Work, Energy, Force)
ùYlT Gi kcal/kgf°C _øp/¨ëhPu/ J/N.°K
¥¡¬ ùLp®u
ùYlTdLPjRp kcal/mh°C _øp ÁhPo/ J/ms°K
®ûN (Force) ®]ô¥/¥¡¬ ùLp®u
C.G.S. Øû\«p : ®ûN (ûPu) = ̈ û\ (gm) X ØÓdLm (ùN.Á/®]ô¥2)
F.P.S. Øû\«p: ®ûN (TÜiPp) = ̈ û\ (Ib) X ØÓdLm (A¥/®]ô¥2)
M.K.S Øû\«p : ®ûN (¨ëhPu) = ¨û\ (Kg) x ØÓdLm (Á/®]ô¥2)
ARu ùTôÚs 1 ûPu = 1 ¡Wôm x1 ùN.Á/®]ô¥2
1 TÜiPp = 1 TÜuh x 1 A¥/®]ô¥2
1 ̈ ëhPu = 1 ¡úXô x 1 ÁhPo/®]ô¥2 = 105
ûPuLs
1 ¡Wôm GûP = 981 ûPuLs
1 TÜih GûP = 32 TÜiPp
1 ¡úXô GûP = 9.81 ¨ëhPuLs
C
V ªu ùTôhùPu£Vp V úYôph V(W/A)
E ªu²VdÏ ®ûN V úYôph V(W/A)
I ªuú]ôhPm A Bm©Vo A
R ªu RûP Ω Km Ω (V/A)
e CûQ ªu RûP Ω m Km ÁhPo Vm/A
G LuPdPuv Ω-1 ºùUuv S
ªu A[ÜLs (Electrical Quantities)
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.1.03
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¿[m, ¨û\, ®ûN, úYûX, §\u Utßm Bt\ûX UôtßRpT«t£ 1.1.04
1 ¸úZ ùLôÓdLlThÓs[ûYLû[ UôtßL
a 5 ùL_eLû[ ÁhPWôL Uôtß
b 15 ûUpLû[ ¡úXô ÁhPWôL Uôtß
c 7 ÁhPûW ùL_UôL Uôtß
d 320 ¡úXô ÁhPûW ûUXôL Uôtß
2 UôtßL
a 5 TÜiÓLû[ ¡úXô¡WôUôL Uôtß
b 8.5 ¡úXô¡WôûU TÜiPôL Uôtß
c 5 AÜuûN ¡WôUôL Uôtß
d 16 PuLû[ ¡úXô¡WôUôL Uôtß
3 UôtßL
a 40 AeÏXjûR ùNi¥ÁhPWôL Uôtß
b 12 A¥ûV ÁhPWôL Uôtß
c 5 ÁhPoLû[ AeÏXUôL Uôtß
d 8 ÁhPoLû[ A¥VôL Uôtß
4 UôtßL
a 234 L]ÁhPûW úLX]ôL Uôtß
b 2 L]A¥ûV ≠hPWôL Uôtß
c 2.5 úLXuLû[ ≠hPWôL Uôtß
d 5 ≠hPoLû[ úLX]ôL Uôtß
5 ¸rLiP úLs®LÞdÏ ®ûP A°dLÜm
a 120°C = ______ °F.
b 8 ª.Á = ______ AeÏXeLs
12 ª.Á =______ AeÏXeLs
6 UôtßL Utßm LiÓ©¥dLÜm
JÚ Lôo 40 ûUpLs TVQm ùNnYRtÏJÚ úLXu G¬ ùTôÚs úRûYlTÓ¡\Õ.
CúR Lôo 120 ¡úXô ÁhPo TVQmùNnYRtÏ GjRû] ≠hPo G¬ùTôÚsúRûYlTÓm.
7 ùLôÓdLlThP ùUh¬d AXÏLÞdÏN¬Vô] ©¬h¥x AXÏLs VôûY?
a ®]ô¥, ¨ªPm, U¦
b ¡Wôm, ¡úXô¡Wôm
c ≠hPov, L] ÁhPoLs
d NÕW ùNu¥ÁhPo, NÕW ¡úXô ÁhPo
8 ¸rLiP ÑÚdLj§u ®¬YôdLj§û]GÝRÜm
a km/L
b N/m2
c KW
d m/S2
e RPM9 ¸r LiPYtû\ NoYúRN AXÏL°p Uôt±
GÝRÜm
a ¿[m
i 3.4 ÁhPo = ______ ª.Á
ii 1.2 ÁhPo = ______ ùN.Á
iii 0.8 ÁhPo = ______ ª.Á
iv 0.02 ¡úXô ÁhPo = ______ ùN.Á
v 10.2 ¡úXô ÁhPo = ______ ûUp
vi 6 ÁhPo = ______ ¡.ÁhPo
vii 18 ÁhPo = ______ ª.Á
viii 450 ÁhPo = ______ ¡. ÁhPo
ix 85 ùN.Á = ______ ¡. ÁhPo
x 0.06 ¡úXô ÁhPo = ______ ª.Á
b ¨û\
i 650 ¡Wôm = ______ ¡úXô ¡Wôm
ii 300 ùNu¥¡Wôm = ______ ¡Wôm
iii 8 ¡Wôm = ______ ùP£ ¡Wôm
iv 120 ªp≠¡Wôm = ______ ¡Wôm
v 8 ùPdLô¡Wôm = ______ ªp≠ ¡Wôm
vi 2.5 ¡Wôm = ______ ªp≠ ¡Wôm
vii 2.5 ¡Wôm = ______ ¡úXô ¡Wôm
viii 20 ùNu¥ ¡Wôm = ______ ªp≠ ¡Wôm
ix 0.05 ùUhôõd Pu = ______ ¡úXô ¡Wôm
c ®ûN
i 1.2 ̈ ëhPu = ______¡úXô ¡Wôm
ii 2.6 ̈ ëhPu = ______ ¡úXô ¡Wôm
iii 800 ̈ ëhPu = ____ ¡úXô ¨ëhPu
iv 14.5 ¡úXô ¡Wôm = ______ ̈ ëhPu
v 25 ¡úXô ¡Wôm = ______ ̈ ëhPu
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d úYûX, Bt\p, ùYlT A[Ü
i 2 ̈ ëhPu ÁhPôó = ______ ̈ ëhPuùNu¥ ÁhPôó
ii 50 ̈ ëhPu ùNu¥ ÁhPôó=_________¨ëhPu ÁhPôó
iii 120 ¡úXô _øp = ______ _øp
iv 40 _øp = ______ ¡úXô _øp
v 300 YôhvAYôó = ______ ¡úXô Yôhv AYo
e §\u
i 200 ùULô Yôhv = ______ Yôhv
ii 0.2 ¡úXô Yôhv = ______ Yôhv
iii 300 ¡úXô Yôhv =____ùULô Yôhv
iv 2.106 Yôhv =____ùULô Yôhv
v 6.10-4 ¡úXô Yôhv = ______ Yôhv
vi 2 Yôhv =____¡úXô Yôhv
vii 350 Yôhv =____¡úXô Yôhv
viii 0.08 Yôhv =____¡úXô Yôhv
ix 2 x 10-3 ¡úXô Yôhv=______ Yôhv
x 0.04 Yôhv =____ùULô Yôhv
f úRûYdÏ Ht\Yôß UôtßL
i 3 ̈ ëhPu ÁhPôó = ______ _øp
ii 2 _øp = ______ Ws
iii 12 _øp = ______¡úXô _øp
iv 3 ̈ ëhPu = _____øp/®]ô¥
v 5 ̈ ëhPu =___________¡úXô ̈ ëhPu
vi 3 ¡úXô _øp = ______ ̈ ëhPu ÁhPo
vii 18 _øp/®]ô¥ = ______ Yôhv
viii 12 Yôhv = __________ _øp/ ®]ô¥
ix ¡úXô _øp/®]ô¥ = ______ ¨ëhPu ÁhPôó/®]ô¥
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.1.04
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16
LôW¦Ls, HCF, LCM Utßm LQdÏLs T«t£ 1.2.05
TLô Gi Utßm ØÝ GiLs (Primenumbers and whole numbers)
LôW¦ (Factor)
LôW¦ GuTÕ JÚ £±V Gi. CRu êXmùTôõV GiLû[ NôõVôL YÏdL CVÛm.ERôWQm
24, 72, 100 GiL°u LôW¦Lû[d LiÓ©¥
24 = 2 x 2 x 2 x 3
72 = 2 x 2 x 2 x 3 x 3
100 = 2 x 2 x 5 x 5
2,3,5 B¡V GiLs LôW¦LsBÏm.
TLô LôW¦«u YûWVû\ (Definintion of aprime factor)
TLô LôW¦ GuTÕ JÚ Gi. AûR TLôGiQôp YÏjRôp LôW¦ ¡ûPdÏm.ERôWQm
57 = 3 x 19
3 Utßm 19 B¡V GiLs TLô LôW¦L[ôÏm.
3 Utßm 19 B¡V GiLû[ TLô GiTh¥V≠p YÚYRôp AYtû\ TLô GußmAûZdLXôm.
H.C.F GuTRu YûWVû\ (Definition of H.C.F)
CÕ A§LThN ùTôÕd LôW¦. GiL°uùRôÏl©p Es[ GpXô GiLÞm NôõVôLYÏdLlTÓm LôW¦VôÏm. ERôWQm.
24, 72, 100 B¡V GiL°u HCFI LiÓ©¥
24 = 2 x 2 x 2 x 3
72 = 2 x 2 x 2 x 3 x 3
100 = 2 x 2 x 5 x 5
êuß GiL°Ûm ùTôÕYô] LôW¦LsBÏm. ARôYÕ 2 x 2 = 4. So HCF = 4.
Áf£ß UPeÏ GuTRu YûWVûW(Definition of L.C.M)
ªLf£±V ùTôÕYô] ùTÚdÏ Gi
Áf£ß UPe¡àûPV ùRôÏl× Gi £±VGiQôL CÚdÏm. ùLôÓdLlThPùRôÏl©u JqùYôÚ GiÔm ÁRmCpXôUp CÚdÏm. ERôWQm
• ¸r LiP GiLÞdÏ LôW¦Lû[LiÓ©¥
7,17,20,66,128
7,17 - B¡V CWiÓm TLô GiûQf úNôókRÕ.CûYLÞdÏ LôW¦Ls úRûY CpûX.B]ôp CûY JúW C]m.
20 þu LôW¦Ls = 2 x 2 x 5
2 663 33
11
2 1282 642 322 162 82 4
2
66 þu LôW¦Ls = 2 x 3 x 11
2 783 39
13
128 þu LôW¦Ls = 2 x 2 x 2 x 2 x 2 x 2 x 2
2 1282 642 322 162 82 4 2
• 3 ØRp 29 YûW Es[ GiL°u TLôGiLû[ úRôóÜ ùNn.
3,5,7,11,13,17,19,23,29,
• ¸rdLiP ÏÝ GiL°u (78, 128, 196) HCF-Id LiÓ©¥
78=2x3x13
2 1962 98
49
2 202 10
5
128=2x2x2x2x2x2x2
196 = 2x2x49
LCM = Áf£ß UPeÏ Á.£.U
HCF = A§LThN ùTôÕdLôW¦A.ùTô.Lô
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2 84, 92, 762 42, 46, 383 21, 23, 19
7, 23, 19
2 36, 108, 602 18, 54, 303 9, 27, 153 3, 9, 5 1, 3, 5
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.2.05
HCF = 2
• 84,92,76 B¡V GiL°u Áf£ß UPeûLLiÓ©¥ (LCM)
LCM =
Áf£ß UPeÏ = 2 x 2 x 3 x 7 x 23 x 19 = 36708
• 36, 108, 60 B¡V GiL°u Áf£ß UPeûLLiÓ©¥ (LCM)
Áf£ß UPe¡u Gi (LCM)
36, 108, 60 = 2 x 2 x 3 x 3 x 3 x 5 = 540
©u]eLû[d L¯dÏm ùTôÝÕ UtßmáhÓm ùTôÝÕ LCM Utßm HCFLiÓ©¥lTRu úRûY HtTÓm.
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18
©u]eLs T«t£ 1.2.06
®YWm (Description)
Ïû\kR A[Ü B]ôp AûY ØÝ Gi ApX.
ERôWQm Gu\ ©u]m GuTÕ ùRôϧ
Utßm TϧûV ùLôiÓs[Õ.
ùRôϧ/Tϧ (Numerator/Denominator)
úLôh¥tÏ úUúX Es[ Gi NôRôWQ©u]j§p ¸úZ Es[ Gi¦u U§l©pEs[ TeLôÏm ERôWQm.
C§p 1,3,7 - GuTûY ùRôϧVôÏm (Numerators)4,12 - GuTûY TϧVôÏm (Denominators).
©u]m : LÚjÕÚ (Fraction: Concept)
JqùYôÚ GiûQÙm ©u]UôL©W§¨§jÕYlTÓjRXôm. ERôWQm.
, JÚ ØÝ GiûQ ©u]UôL
©W§¨§jÕYlTÓjRXôm. (TPm 1)
ùTÚdLp (Multiplication)
©u]eLû[ ùTÚdÏm ùTôÝÕ GpXôTϧLû[Ùm ùTÚd¡]ôp, TϧL°uùTÚdÏ ùRôûL ¡ûPdÏm Utßm GpXôùRôϧLû[Ùm ùTÚd¡]ôp, ùRôϧL°uùTÚdÏ ùRôûL ¡ûPdÏm (TPm 3)
©u]m: U§l× (Fraction:Value)
©u]j§u TϧûVÙm, ùRôϧûVÙm JúWGiQôp YÏjRôúXô ApXÕùTÚd¡]ôúXô ©u]j§u U§l× Uô\ôÕ(TPm 2)
YÏjRp (Division)
JÚ ©u]jûR Utù\ôÚ ©u]jRôp YÏdL.YÏdÏm ©u]jûR RûX ¸ZôL Uôt±YÏTÓm ©u]júRôÓ ùTÚdL úYiÓm.(TPm 4)
áhPp Utßm L¯jRp (Addition andSubraction)
©u]eLû[ áhP (A) L¯dL AYt±u TϧNUUôL CÚdL úYiÓm. TϧLs ANUUôLCÚl©u AûR Áf£ß UPeLô] TϧVôLUôt\ úYiÓm. CûR JqùYôÚ ©u]j§uTϧVôÛm YÏjÕ DûY ùRôϧVôp ùTÚd¡áhP úYiÓm (TPm 5)
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ERôWQm
• ùTÚdLp
• YÏjRp
• áhPp
p CÚkÕ I L¯dLÜm
©u]eL°u YûLLs (Types of fractions)
• RÏ©u]j§u ùRôϧ TϧûV®PGlùTôØÕm Ïû\YôLLúY CÚdÏm.
RLô©u]j§u ùRôϧ TϧûV®PA§LUôL CÚdÏm.
LXl× ©u]m GuTÕ JÚ ØÝ GiÔm,RÏ©u]Øm LXkR Jo GiQôÏm.
©u]jûR áhÓRp (Addition of fraction)
áhPp
CkR ©u]jûR áhP, Sôm 2,8,12 B¡VTϧL°u Áf£ß UPeûL (LCM) LiÓ ©¥dLúYiÓm.
2,8,12 u Áf£ß UPeûL LiÓ ©¥dLÜm.
vùPl 1 Áf£ß UPeÏ Gi
2 2,8,122 1,4,6
1,2,3
LôW¦Ls 2,2,2,3
BûLVôp Áf£ß UPeÏ Gi
= 2 x 2 x 2 x 3 = 24,
vùPl 2
©u]jûR L¯jRp (Subtraction of fractions)
≠ÚkÕ - I L¯ (A)
vùPl 1: ØÝ GiûQ ØR≠p L¯dLÜm 17 - 9 = 8
vùPl 2 : 16,32 = 32 dLô] Áf£ß UPeÏ (LCM) 32
32 Gu\ Gi 16 Gu\ GiQôp YÏTÓYRôp
Gu\ ©u]m ¡ûPdÏm.
vùPl 1 u T¥ ØÝ GiûQ úNodÏmùTôÝÕ.
SUdÏd¡ûPlTÕ
NôRôWQ ©u]eLs (Common fractions)
áhPp ϱ Utßm L¯jRp ϱ ùLôiPLQdÏLs.
ERôWQm
¾oÜ Lôi
¸r LiP ®§Lû[ LûP©¥dLÜm.
1 GpXô ØÝ GiLû[Ùm áhPÜm
2 áhPp ϱ (+) Es[ GpXô GiLû[ÙmáhPÜm.
3 L¯jRp ϱ (-- - -) Es[ GpXô GiLû[ÙmáhPÜm.
4 GpXô TϧL°u Á.£.U -ûYLiÓ©¥dLÜm.
¾oÜ
vùPl 1 : ØÝ GiLû[ áhPÜm= 3 + 6 - 4 = 5
vùPl 2 : ©u]eLû[ áhPÜm= 3/4 + 7/8 - 5/16 - 9/32
Á.£.U. Gi: 4,8,16,32 is 32
3217
16 7
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.2.06
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20
vùPl 3: ÁiÓm ØÝ GiLú[ôÓ áhÓmùTôÝÕ..
SUdÏ ¡ûPlTÕ
AûPl×Ls Utßm ARu ¾oÜLs (Bracketsand their solution)
CWiÓ ApXÕ CWi¥tÏ úUtThP ©u]dáßLû[ £XNUVm áhÓYRtúLô ApXÕL¯lTRtúLô AûPl×dϱ TVuTÓjRlTÓ¡\Õ. AûPl©tÏs CÚlTûYLû[ ¾oÜLôiTRtÏ ‘BODMAS’ Gu\ ®§TVuTÓjRlTÓ¡\Õ.
BODMAS ®§
• B - ©WôdLh CûR ØR≠p ùNnV úYiÓm.
• O -of CWiPôYRôL
• D - YÏjRp êu\ôYÕ
• M - ùTÚdLp SôuLôYÕ
• A - áhPp IkRôYRôL
• S - L¯jRp LûP£VôL ùNnV úYiÓm
AûPl×Ls Es[ LQdÏ
¾oÜ Lôi
• YÏjRp (Division)
a
b
• áhPp (Additions)
• L¯jRp (Subract)
¸rLiP vùPl©û] LûP©¥dLÜm.
( ) 1 Es TdL AûPlûT ¾odLÜm ( )
2 ùTÚdLp Utßm YÏjRûX Ju\ôL¾odLÜm
3 áhPp Utßm L¯jRûX Ju\ôL¾odLÜm
{ } 4 LûP£ ¨ûXdÏ úTôÏm ØuYû[Yô] AûPlûT ¾odLÜm.
[ ] 5 LûP£VôL NÕW AûPlûT ¾odLÜm.
ERôWQeLs
NôRôWQ ©u]eLs (Common fractions)
• ùTÚdLp (Multiply)
a
b
14
3
7
4x
8
3
7
4by
8
3==
⎥⎥⎦
⎤
⎢⎢⎣
⎡
⎭⎬⎫
⎩⎨⎧
⎟⎠⎞
⎜⎝⎛ −+−+
21
872116810
12308
123810
8
315810
8
31580
==
=
+
××
⎥⎦⎤
⎢⎣⎡ ×
⎥⎦
⎤⎢⎣
⎡⎭⎬⎫
⎩⎨⎧= 1
2
1367
4
2367
4
1470
4
4956
4
11256
4
119456
4
1
2
119456
=
=
=
×=
×=
+−+=
−+−+
⎥⎦⎤
⎢⎣⎡
⎥⎦⎤
⎢⎣⎡
⎥⎦
⎤⎢⎣
⎡⎭⎬⎫
⎩⎨⎧
⎥⎦
⎤⎢⎣
⎡
⎭⎬⎫
⎩⎨⎧
⎟⎠⎞
⎜⎝⎛
AûPl×Ls Es[ LQdÏ (Bracket problems)
• ¾ôóÜ Lôi
‘BODMAS’ ®§ûV TVuTÓj§ ¾oÜ LôiL.
• ‘BODMAS’ ®§ûV TVuTÓj§ ¾oÜ LôiL.
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.2.06
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21
RNU ©u]eLs T«t£ 1.2.07
®[dLm (Description)
RNU ©u]m GuTÕ JÚYûL ©u]mARàûPV Tϧ 10 (A) 10 u ùTÚdÏ ùRôûL(ARôYÕ) 10,100,1000, 10,000 ØR≠VûY RNUGiLÞdLô] ùTôÚ[ôÏm.
12.3256 GuTÕ
©W§¨§jÕYm (Representation)
C§p Tϧ ¡ûPVôÕ Tϧ«u A[ÜU§l©û]l ùTôÚjÕ, RNU ×s°LsTpúYß ¨ûXL°p ϱl©PlTÓ¡\Õ.
ERôWQm.
3.648
1000
36480.0127,
10000
1270.35
100
350.5,
10
5====
áhPp Utßm L¯jRp (Addition andsubtraction)
RNU ©u]j§u ×s°Ls ùNeÏjÕY¬ûN«p ûYdLlTÓ¡\Õ. JqùYôÚ©u]jûRÙm áhÓm ùTôÝÕ (A) L¯dÏmùTôÝÕ AÓjRÓjÕ ARu ¸rûYdLlTÓ¡\Õ. CRu êXm GpXô RNU×s°LÞm úSoY¬ûN«p ûYdLlTÓ¡\Õ.áhÓm ùTôÝúRô (A) L¯dÏm úTôúRô ØÝGiLÞdÏ LûP©¥lTÕ úTôp RNU×s°L°u Y¬ûNdÏ ¸úZ ϱjÕ ®ûPA°dL úYiÓm.
RNU ©u]eLs JußdÏ Ïû\YôL CÚkRôp,RNU ×s°dÏ Øu× é_óVm ϱdLúYiÓm.ERôWQm: 45/100 = 0.45 (ùYßUú] .45 Gu\GÝRdáPôÕ)
áhÓL 0.375 + 3.686
0.375
3.686
4.061
L¯dLÜm 22.61 p CÚkÕ 18.72 I L¯dLÜm.
22.61
18.72 3.89
ùTÚdLp (Multiplication)
RNU ×s°Lû[ LiÓùLôs[ôUp ØÝGiLû[ ùTÚdL úYiÓm. RNU ×s°dÏ
YXÕ TdLm ùUôjRm GjRû] CXdLmEs[Õ GuTûR LY²dL úYiÓm. CkRRNU ×s°ûV YXÕ TdLj§p CÚkÕ Ï±dLúYiÓm.
ùTÚdÏL 2.5 by 1.25
= 25 x 125 = 3125. YXÕ TdLj§p RNU×s°«u áhÓj ùRôûL 3. AR]ôp ARu®ûP 3.125
YÏjRp (Division)
ØÝ GiQôL Uôt\ RNU ×s°ûV YXÕTdLUôL SLôój§ ûYdL úYiÓm. RNU×s°Lû[ ©ôõjÕ AúR Gi¦dûL«pAûUdL úYiÓm. úRûYlThPôpé_ó_õVjûR úNôódLÜm. ©\Ï YÏdLÜm.
0.75 I 0.25 Bp YÏdLÜm.
37525
25
75
100
100x
0.25
0.75
0.750.25
=
=
RNU ×s°ûV ùTÚdL, ùTÚdÏ Gi10 BL CÚkRôp, Gi¦dûLdÏYXÕ TdLm JÚ CPm Rs° SLôójRúYiÓm. Gi 100 BL CÚkRôpCWiÓ CPm Rs° ûYdL úYiÓm.AúR Uô§ôõ ùTÚdÏ 1000þdÏm UtßmCúRúTôp ϱdL úYiÓm. 10 þBpYÏjRôp RNU ×s°ûV JÚ CPmCPÕ TdLm Rs° AûUdLúYiÓm. CÕúY 100 BL CÚkRôp,CWiÓ CPj§tÏ RNU ×s°ûVSLôój§ ûYdL úYiÓm UtßmCûRúV ùRôPWúYiÓm.
ERôWQm
900 ª.Á ¿[Øs[ Tôôõp JqùYôÚ ÕiÓùYhÓYRtÏm 3 ªÁ A§LUôL ûYjÕGÓjÕd ùLôiPôp GjRû] ©uLs¡ûPdÏm? ùTôÚ°p ÁR ¿[m GqY[ÜCÚdÏm?
1 ©u²u ¿[m
= 2.25 + 55.36 + 15.18
= 69.79 ª.Á
Tô¬u ¿[m = 900 ª.Á
© NIMI, Not to be republished
22
©u]jûR RNUUôL Uôtß
ERôWQm
• ©u]jûR RNUUôL Uôt\Üm.
I NôRôWQ Øû\«p YÏdLÜm, B]ôp
é_ó_õVjûR (úRûYVô] A[®tÏ) 9Gi¦tÏ (Numerator) ©\Ï AûUdLÜm.
169
=0.5625
• I RNU©u]UôL UôtßL
0.875
0 40 40
56 60
6470008
ÑZp RNU ©u]m (Recurring decimals)
©u]j§p CÚkÕ RNU ©u]j§tÏ UôtßmùTôÝÕ £X ©u]eLû[ N¬Vô] RNU©u]j§tÏ YÏdL Ø¥Ùm. £X ©u]eL°pDÜ Ø¥®pXôUp ùRôPÚm CR]ôp CRtÏÑZp ©u]m Guß ùTVo.
vùPl 1
ùYhPlTP úYi¥V ©u²u Gi¦dûL= X
X Gi¦dûL Es[ ©u²u ¿[m= X x 69.79 ªÁ
vùPl 2
JqùYôÚ ©uàdÏm HtTÓm L¯Ü = 3 ªÁ
L¯Ü x ©u²u Gi¦dûL= 3 x X ªÁ = 3XªÁ
(1) + (2) - I áh¥ Utßm Lm©«u ¿[j§tÏNUuTÓjRÜm.
69.79 X ªÁ + 3 X ªÁ = 900 ªÁ
X (69.79 ªÁ + 3 ªÁ) = 900 ªÁ
X (72.79 ªÁ) = 900 ªÁ
X = 900 ÷ 72.79
12 ©uLs ùNnV CVÛm
CWiPôYRôL
ÁRm Es[ ùTôÚ°u ¿[m.
= Lm©«u ùUôjR ¿[m – 12 ©uL°u¿[m + ùYhÓm ùTôÝÕ HtTÓmL¯ÜLs.
= 900 ªÁ – (12 x 69.79 + 12 x 3) ªÁ
= 900 – (837.48 + 36) ªÁ
= 900 – 873.48
= 26.52 ªÁ
ÁRm Es[ Lm© = 26.52 ªÁ
RNUj§p CÚkÕ ©u]j§tÏ UôtßRp AúRUô§¬ §Úl© ùNnRp
RNUjûR ©u]UôL Uôtß.
ERôWQm
0.375 I ©u]UôL Uôtß
1 I ̧ úZ ϱdLÜm, AûRj ùRôPokÕ êußCXdLj§tÏ êuß é_ó_õVm ϱdLÜm.
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.2.07
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23
ERôWQm
• UôtßL
a ÑZp RNUm
b ÑZp RNUm
c
CûYLs GiL°u ÁÕ ×s° ûYjÕ ¸úZEs[T¥ GÝRlTÓ¡\Õ.
0.3333 ——> 0.3
0.6666 ——> 0.6
0.14857142 —> 0.14857
LY²dL : ×s°Ls GiLs ÁÕûYdLlTÓ¡\Õ.
ùTô±«Vp Õû\«p LQd¸Ó ùNnÙmùTôÝÕ ùTôÕYôL SôuÏ RNUm YûW RNU×s°Ls ûYlTÕ EiÓ.
LQd¸Ó ùNnVlThP A[ÜL°uU§l©u úRôWôVm (Approximations in M.V.calculations)
M.V.LQd¸ÓL°p SôuÏ RNU CPeLú[úTôÕUô]ûY G²àm TWôU¬l×úYûXL°p CVk§Wj§u TôLeLÞdÏA[ÜLs ϱdÏm ùTôÝÕ ùTÚmTôÛmêuß RNU CPeLú[ úTôÕUô]RôÏm.
úRôWôVUô] RNUeLû[ GÝÕm Øû\
1.73556 = 1.7356 SôuÏ RNUeLÞdÏ N¬VôL
5.7343 = 5.734 êuß RNUeLÞdÏ N¬VôL
0.9345 = 0.94 CWiÓ RNUeLÞdÏN¬VôL
10,100,1000 B¡VYt\ôp ùTÚdLp UtßmYÏjRp (Multiplication and division by 10,100,1000)
RNUjûR 10 Bp ùTÚdÏRp.
RNU ©u]jûR 10,100,1000 úTôu\ GiL[ôpùTÚdÏm ùTôÝÕ, RNU ×s°Lû[ YXÕTdLj§p ûYdL úYiÓm. ùTÚdLÛdÏHt\Yôß é_ó_õVjûR ûYdL úYiÓm.
• 4.645 x 10 = 46.45 (JÚ CPm)
• 4.645 x 100 = 464.5 (CWiÓ CPm)
• 4.645 x 1000 = 4645 (êuß CPm)
RNUjûR 10 Bp YÏjRp
RNU ©u]jûR 10,100,1000 úTôu\ GiL[ôpYÏdÏm ùTôÝÕ, RNU ×s°ûV CPÕ TdLmSLoj§ ûYdL úYiÓm. YÏjRÛdÏ Ht\Yôßé_ó_õVjûR ûYdL úYiÓm.
ERôWQeLs
• 3.732 ÷ 10 = 0.3732 (JÚ CPm)
• 3.732 ÷ 100 = 0.03732 (CWiÓ CPm)
• 3.732 ÷ 1000 = 0.003732 (êuß CPm)
ERôWQm
• ¸rLiP GiLû[ ©u]eL[ôL ÁiÓmGÝÕL.
453.273
453.273
• ùLôÓdLlThP Gi 0 .386 - - -- dÏ RNUCPj§u ̈ ûX«û] GÝRÜm.
3 - ØRp RNU CPm
8 - CWiPôYÕ RNU CPm
6 - êu\ôYÕ RNU CPm
• ¸rLiP RNUjûR, êuß CPeLÞdÏúRôWôVUôL GÝRÜm.
a 6.9453 ——> 6.945
b 8.7456 ——> 8.746
• ©u]eLû[ RNU ©u]UôL Uôtß
• RNU ©u]jûR ©u]UôL Uôtß
ÑZp RNUm
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.2.07
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24
§\]ônÜ T«t£ (Assignment)
1 ¸rLiP RNU GiLû[ ®ôõYôdL Øû\«pGÝÕL.
a 514.726
b 902.524
2 ¸rLiP ®ôõYôdL Øû\«p Es[ RNUGiLû[ RNU ©u]UôL GÝÕL
a
b
3 ¸rLiP RNU ©u]eLû[ NôRôWQ©u]UôL G°V Øû\«p UôtßL
a 0.72
b 5.45
c 3.64
d 2.05
4 ¸rLiP ©u]eLû[ RNU ©u]UôLUôtßL
a
b
c
d
e
f
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.2.07
© NIMI, Not to be republished
25
TôdùLh LôpÏúXhPo Utßm ARu TVuTôÓLs T«t£ 1.2.08
L¥]Uô] LQdÏLû[ Ïû\kR úSWj§pTôdùLh LôpÏúXhPo êXm ¾oÜ LôQCVÛm. JÚ NôRôWQ LôpÏúXhPWôp, L¦RNmTkRUô] LQdÏLs ARôYÕ áhPp,L¯jRp, ùTÚdLp Utßm YÏjRpB¡VûYLû[ ¾odLXôm, G²àm®gOô]m Utßm ùRô¯p ÖhT LôpÏúXNàdÏ ®gOô] LôpÏúXhPûWTVuTÓjRXôm.
LôpÏúXhPûW TVuTÓjÕYRtÏ £\l×T«t£ GÕÜm úRûY CpûX. B]ôpLôpÏúXhPo úYûX ùNnÙm ®RjûRúUàYp êXm AdLû\ÙPu T¥jÕ ùR¬kÕùLôsYRu êXm ARu ØÝûUETúVôLjûR TVuTÓj§d ùLôs[Xôm.LôpÏúXhPo ÑVUôL £k§dLôÕ UtßmùNVpTPôÕ, CVdÏTYu ׬kÕ ùLôiÓLQdÏLû[ ̧ êXm LôpÏúXhPûW N¬VôLCVdL úYiÓm.
LhPûUdLlThP ®[dLeLs (TPm 1)
¸úTôoPô]Õ ARu TWlûT ÑXTUôL׬kÕdùLôsÞm YûL«p 5 BL ©¬dLlThÓs[Õ.
• úPhPô Gi¼Ã ¸ - Ls
Gih¥¬ ¸-Ls 0 ________ ØRp 9 YûWCÚdÏm.
RNU ×s°«u ¸ .
• ¡°V¬e ¸ - Ls
CkR ¸«p ‘C’ GÝjÕ CÚdÏm
¡°Vo úPôhP≠C CLR
CE
CM MC
áhPp ¸
L¯jRp ¸
ùTÚdLp ¸
YÏjRp ¸
NUUô] ¸, ®ûPûV A±®dÏm ¸=
¡°Vo ùUúUô¬
+
—
x
÷
• @Te`u ̧ (Function keys)
ûT ¸
x YodL êXm ¸
NRÅRm ¸
ϱûV Uôtßm ¸
YodLj§u ¸
TWvTWm ¸ (ùW£×úWôdLp ¸)
π
%
+/-
x2
1x
• ¨û]Ü ¸ - Ls (Memory keys)
¥v©ú[ GiLû[ úNªjRp
¥v©ú[ U§lûT ùUúUô¬Ù-Pu áhÓYRtÏ
¥v©ú[ U§lûT ùUúUô¬«pCÚkÕ L¯lTRtÏ
úNªjR U§lùTiLû[ÁiÓm ¥v©ú[«p ùLôiÓYÚRp
M
M+
M-
MR RCL
¡°Vo GuP¬ UhÓm
úUÛm TX úYûXLs ùNnÙm @TeL`]p¸-Ls N«u¥©d LôpÏúXhP¬p AûUdLlThÓs[ûR TPm 2 LôhÓ¡\Õ.
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ØdúLôQ®Vp ùNVp-TôÓLs UtßmAûPl× Ï±Ls ùNVpTôh¥tLôL
£X ¸ L°p LXo GÝjÕdLs ¸úZApXÕ úUúX AûUkÕ CÚdÏm. LXoGiLû[ TVuTÓjR INV ¸ûVAÝjRÜm. ¥v©ú[«p INVúRôu±V©\Ï ̧ ûV AÝj§]ôp LXoGÝjÕLû[ AÕ C]mLiÓùLôsÞm. ¥v©ú[«p CÚkÕ INVClùTôÝÕ Uû\kÕ®Óm.
CRu êXm ¥v©ú[ GiÔdÏ UPdûL U§l×m LôQXôm Utßm, ¥v©ú[ U§l©tÏ G§o UPdûL GiûQÙm LôQXôm.
¥v©ú[«p ùR¬Ùm ùNqYLúLôBo¥ú]h¥p CÚkÕúTôXôo úLô Bo¥ú]h BLUôtßYRtÏ.
¥v©ú[«p ùR¬Ùm úTôXôoúLô Bo¥ú]h¥p CÚkÕùNqYL úLô Bo¥ú]hÓdÏUôtßYRtÏ.
• ¥v©ú[
Cu×h úPhPô, CûP úSW Ø¥Ü, UtßmLQd¡u ®ûPLs ¥v©ú[«p LôhÓm.
TWl©p AûUdLlThPûYLsJqùYôÚ RVô¬l©Ûm UôßThÓCÚdÏm. EXL A[®p GiLs JÚϱl©hP YûL«pRôu AûUdLúYiÓm Guß Ø¥Ü ùNnVlThÓs[Õ. ARuT¥Rôu 10 GiLsùNhPôL AûUdLlTÓ¡\Õ.
Sin Cos Tan ( )
Exp GdvúTô]uh ̧
INV
log INV 10x
INV R–P
INV P–R
= 23.9
®§Ls Utßm ERôWQeLs :
• áhPp : ERôWQm 18.2 + 5.7
• YÏjRp : ERôWQm 18.5/2.5
YÏTÓm GiLû[AÝjRÜm
÷ ¸ûV AÝjRÜm
YÏjRp GiLû[ AÝjRÜm. YÏTÓm Gi T§ÜùNnVlTÓm.
= ̧ ûV AÝjRÜm
+
=
Y¬ûNlT¥ Cu×h ¥v©ú[
18.5
18.5
2.5
7.4
.
.
1 8 5
52
ùTÚdLlTÓm GiLû[AÝjRÜm
x ̧ ûV AÝjRÜm
ùTÚdLp GiLû[AÝjRÜm
= ̧ ûV AÝjRÜm
Y¬ûNlT¥ Cu×h ¥v©ú[
• ùTÚdLp : ERôWQm 0.47 x 2.47
. 4 7
x
2 . 4 7
=
0.47
0.47
2.47
1.1609
ØRp Y¬ûN ϱdLÜm
— ̧ ûV AÝjRÜm
L ¯ d Ï m G i L û [AÝjRÜm
= ̧ ûV AÝjRÜm
• L¯dLÜm : ERôWQm 128.8 — 92.9
Y¬ûNlT¥ Cu×h ¥v©ú[
128.8
128.8
92.9
35.9
1 2 8 . 8
-
9 2 . 9
=
áhÓj ùRôûL«uY¬ûNûV AÝjRÜm
+ ̧ ûV AÝjRÜm
C W i P ô Y Õá h Ó j ù R ô û L « uY¬ûNûV AÝjRÜm
ØRp Y¬ûN T§Ü ùNnVlThÓ CÚdÏm = ¸ûVAÝjRÜm
1 8 . 2
+
Y¬ûNlT¥ Cu×h ¥v©ú[
5 . 7 5.7
= 23.9
18.2
18.2
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.2.08
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27
2.5 AÝjRÜm
x ¸ûV AÝjRÜm
7.2 AÝjRÜm÷ ̧ ûV AÝjRÜm
4.8 I AÝjRÜm
= ̧ ûV AÝjRÜm
¨û]®p ùLôs[Üm:ØRp U§lûT Cu×hùNnYRtÏ Øu©u]j§tÏ ¸úZ Es[úLôhPôp, ¸ûV ùNVp
TÓjR úYiÓm.
1.25 AÝjRÜm
= ̧ ûV AÝjRÜm
1 2 5 1.25.
= 3.0
• ùTÚdLÛm YÏjRÛm :ERôWQm : 2.5x7.2/4.8x1.25
Y¬ûNlT¥ Cu×h ¥v©ú[
2.52 . 5
x
7 . 2
÷
2.5
7.2
1.8
4.8
3.75
8.4
=
• ùUúUô¬ûV úNªjRp : ERôWQm (2+6)(4+3)
Y¬ûNlT¥ Cu×h ¥v©ú[
ØRp AûPl× Ï±ûV 2 2ùNVp TÓjR úYiÓm
+ 2
6 6
= 8
ØRp ®ûPûV úNªdLÜm STO , M 8
x or M+
CWiPôYÕ AûPl× 4 4ϱûV ùNVpTÓjRúYiÓm + 4
3 3
= 7
x ¸ûV AÝjRÜm x 7
ùUúUô¬ûV §ÚmT RCL or MR 8AûZdLÜm
= ̧ ûV AÝjRÜm = 56
Y¬ûNlT¥ Cu×h ¥v©ú[
• NRÅRm : ERôWQm 1500 dÏ 12 NR®¡Rm
1500 I ÖûZdLÜm 1 5 0 0 1500
x ¸ûV AÝjRÜm x 1500
12 I ÖûZdLÜm 1 2 12
INV % AÝjRÜm INV % 12
= ¸ûV AÝjRÜm = 180
a
a
a
Y¬ûNlT¥ Cu×h ¥v©ú[
• YodL êXm : ERôWQm 53 2 ×+
2 I ÖûZdLÜm 2 2
a ̧ ûV AÝjRÜm 2
+ ̧ ûV AÝjRÜm + .
©WôdLh ̧ ûV AÝjRÜm ( .
3 I ÖûZdLÜm 3 3
a ̧ ûV AÝjRÜm .
x ¸ûV AÝjRÜm x .
5 I ÖûZdLÜm 5 5
a ̧ ûV AÝjRÜm .
ê¥V AûPl× ̧ ûV AÝjRÜm ) .
= ̧ ûV AÝjRÜm = 5.2871969
2 + ( 3 x 5 ) = 5.2871969
• ùTôÕYô] UPdûL :ERôWQm Xôd 1.23
1 . 2 3 log = 0.0899051
• UPeÏ : ERôWQm 123 + 302
1 2 3 + 3 0 INV X2 = 1023
Y¬ûNlT¥ Cu×h ¥v©ú[
Y¬ûNlT¥ Cu×h ¥v©ú[
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.2.08
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• LQd¸Ó BWm©dÏm Øu ‘ON’ ¸ûVAÝj§, ¥v©ú[«p ‘0’ ùRôõ¡u\RôGuß TôôódL úYiÓm.
• LôpÏúXhPôõu EhTϧLû[ùRôPdáPôÕ. úYLUôL RhÓYûRR®ôódLÜm. ªLÜm AÝjRUôLAÝjRdáPôÕ
• ùYlT ¨ûX 0° ØRp 40° C YûW«pLôpÏúXhPûW TVuTÓjRÜm.
• B®VôLd á¥V §WYm ARôYÕXôdÏVo, §u]ôó, ùTuûNu B¡VûYLû[d ùLôiÓ, LôpÏúXhPôóTôLeLû[ ÑjRm ùNnVdáPôÕ.
• LôpÏúXhPûW Yû[lTúRôApXÕ¸úZ úTôÓYûR R®odL £\l× LY]mùLôs[Üm.
• CÓl× TôdùLh¥p EuàûPVLôpÏúXhPûW GÓjÕfùNpXdáPôÕ.
§\]ônÜ T«t£ (Assignment)
1 LôpÏúXhPûW TVuTÓj§ ¸úZEs[ûYLû[ ¾ôóÜ ùNn
a 625 + 3467 + 20 + 341 + 6278 = ______
b 367.4 + 805 + 0.7 + 7.86 + 13.49 = ______
c 0.043 + 1.065 + 13.0 + 34.76 + 42.1 = ______
d 47160 + 1368.4 + 0.1 + 1.6901 + 134.267 =_______
2 LôpÏúXhPûW TVuTÓj§ ¸úZEs[ûYLû[ ¾ôóÜ ùNn
a 24367 — 4385 = ______
b 9.643 — 0.7983 = ______
c 4382.01 — 381.3401 = ______
d 693.42 — 0.0254 = ______
3 LôpÏúXhPûW TVuTÓj§ ¸úZEs[Yt±u U§lûT ùNn
a 23 x 87 = ______
b 1376 x 0.81 = ______
c 678 x 243 = ______
d 0.75 x 0.24 = ______
4 LôpÏúXhPûW TVuTÓj§ ¸úZEs[ûYLû[ ¾ôóÜ ùNn
a 22434 ÷ 3 = ______
b 4131 ÷ 243 = ______
c 469890 ÷ 230 = ______
d 3.026 ÷ 0.89 = ______
5 ¸úZ Es[ûYLÞdÏ ¾ôóÜ LôiL
a = ________
b ________
6 ¸úZ Es[ûYLÞdÏ ¾ôóÜ LôiL
a =−+
8x0.30.52)128)x(384(634
________
b =+−
−−−17.04).10.021)x(28(3.89
2.6)0.0512.2)x(842(389 _________
®hPm (ø) = 782 mmúLôQm (α ) = 136°YhPúLôQlTϧ«uTWlT[Ü (A) =
°
=360
αx
4
d x π A
2 ϱl×
TdLm (2a) = 450 ª.Á
TdLm (2b) = 250 ª.Á
¿s YhPj§uÑt\[Ü(c)= _____Á
ϱl× C = )(2 22 ba +π
7
®hPm (d) = 1.25 ÁL] A[Ü(V) = ______ ùP£ Á3
3πr
3
4V =ϱl×
9
10
8
¿[m (L) = 1.2 ÁALXm (B) = 0.6 ÁEVWm (H) = 0.5 ÁG@¡u APoj§ = 7.85 ¡.¡/ùP£Á3
¨û\(m) = ______ ¡úXô¡Wôm(¨û\ (m) = V x r )
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.2.08
© NIMI, Not to be republished
29
LôpÏúXhPûW TVuTÓj§ ¾oÜ LôÔRp T«t£ 1.2.09
1 ¸úZ Es[Ytû\ RLô ©u]UôL UôtßL
a __________7
21 =
b __________534 =
c __________5
33 =
d __________8
75 =
e _________3
13 =
f ______4
35 =
g __________7
37 =
h __________74
1182 =
2 ¸úZ Es[Ytû\ LXl× GiQôL UôtßL
a __________11
12=
b __________14
36=
c __________10
18=
d __________3
25=
e __________13
84=
f __________21
32=
g __________16
18=
h __________4
75=
3 ®ÓThP GiLû[ ̈ Wl×L
a __________91x
1311
=
b __________x
42
5
3=
c __________98
x
14
9=
4 ÑÚdÏL
a _________60
45=
b __________12
8=
c __________14
12=
d __________72
56=
e __________14
6=
f __________6
14x
4
2x
3
11x
7
5x
4
3=
5 ùTÚdLp
a __________32x5 =
b __________2x43
=
c __________65x
43
=
d __________3x413 =
e __________413x
412 =
f __________416x5 =
© NIMI, Not to be republished
30
6 YÏjRp
a _________ 4
3
4
1=÷
b ________ 4
36 =÷
c __________7
2
4
3=÷
d __________46
13 =÷
e ________ =÷7
12
2
15
f _________4
138 ÷
7 ®ÓThP GiLû[ ̈ Wl×L
a x_________12
1
3
2=
b x________121
2414
=
c x_________121
87=
d x_________121
362
=
e x_________121
3652
=
f x_________121
24113 =
g x_________121
43=
h x_________121
67=
8 ¸úZ Es[Ytû\d áhÓL
a _________12
7
4
3=+
b _________4
3
8
7=+
c _________83
54
53
=++
d _________973
1271
416 =++
9 L¯jRp
a _________52
54
=−
b _________43
65
=−
10 ÑÚdÏL
a _________16
11
3
1
8
3
7
62 =−−−
b ________86
5
7
22 =+−
c _________2
12
4
31
5
3
9
73 =+−+−
11 RLô ©u]UôL ùY°lTÓjÕL
a4
35
b64
53
c12
51
12 LXl× GiQôLúYô (A ) ØÝGiQôLúYô Ïû\dLÜm.
a4
163
b4
12
c60
144
13 Ïû\kRThN A[YôL ÑÚdLd LôhPÜm
a64
12
b48
12
c60
144
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.2.09
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31
14 RNUeL°u áhPp
a 4.56 + 32.075 + 256.6245 + 15.0358
b 462.492 + 725.526 + 309.345 + 626.602
15 RNUd L¯jRp
a 612.5200 – 9.6479
b 573.9246 – 215.6000
c 968.325 – 16.482
d 5735.4273 – 364.2342
16 áhPp Utßm L¯jRp
a 56.725 + 48.258 – 32.564
b 16.45 + 124.56 + 62.7 - 3.243
17 RUNeL°u ùTÚdLp
a By 10,100,1000
i 3.754
ii 8.964 x 100
iii 2.3786 x 1000
iv 0.005 x 1000
b ØÝ GiQôp ùTÚdÏRp
i 8.4 x 7
ii 56.72 x 8
c Utù\ôÚ RNUjRôp ùTÚdÏRp(LôpÏúXhPo ETúVô¡dLÜm)
i 15.64 x 7.68
ii 2.642 x 1.562
18 ¸úZ Es[Ytû\ YÏdLÜm
a25
62.5
b9
14.4
c10
64.56
d100
0.42
e1000
48.356
f15
25.5
19 YÏjRp
a1.2
16.8
b1.2
1.68
c1.2
0.168
d1.1
1.54
e1.6
27.2
f 31.5 ÷ 10.5
g 1.54 ÷ 1.1
h 4.41 ÷ 2.1
20 ©u]jûR RNU©u]UôL Uôt\Üm
i 18
5
ii25
12
21 U§lûTd Lôi
20.5 x 40 ÷ 10.25 + 18.50
22
23
24
25
A = 12.613 ªÁX = _________ ªÁ.
X = __________ ªÁ.
X = __________ªÁ.
B = __________ªÁ.
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.2.09
© NIMI, Not to be republished
32
YodLm Utßm YodLêXm T«t£ 1.3.10
a A¥lTûP Gi (Basic number)
2 ϱ Gi (exponent)
YôódL êXj§u AûPVô[m
a2 þu YodLêXm (A) YodLj§u
YodLêXm a2 þu êXm.
YodL Gi (Square number)JÚ YodL Gi GuTÕ JÚ GiRuû]jRôú] AúR GiQôp ùTÚd¡dùLôsYÕ.
A¥lTûP Gi x A¥lTûP Gi = YodLGi
a x a = a2
4 x 4 = 42 = 16
©ôõjRp (Splitting up)JÚ NÕW TWlT[ûY £±V TWl×L[ôL ©ôõdLCVÛm. ªLl ùTôõV NÕWm 36, 16 ùTôõVTWl©u êXUôL LhPûUdLlThÓs[Õ,C§p Es[ £±V NÕWm 4 Utßm 8Gi¦dûL«Ûs[ 2 ùNqYLeLs.
ùTôõV NÕWm 4 x 4 = 16 a2
CWiÓ ùNqYLm 2 x 4 x 2 = 16 2ab
£±V NÕWm 2 x 2 = 4 b2
£±V TWl©u áhÓjùRôûL = 36 = a2 + 2ab + b2
Ø¥Ü: YôódL êXm LiÓ©¥dL YodLGiLû[ Sôm ©ôõdL úYiÓm.
YôódL êXjûR ©¬jùRÓjRÛdLô]ùNnØû\
• CWiÓ GiL°u ùRôÏl©tÏ RNU×s°ûV YXÕ TdLm Utßm CPÕ TdLmûYdL úYiÓm. Ød¡VUô] ϱÂûP
ϱdLÜm.
• ØRp ùRôÏl©tÏ YôódL êXm LôiL.®j§VôNjûR LiÓ©¥jÕ, AÓjRùRôÏl©tÏ ùLôiÓ YWÜm.
• êXjûR (Root) 2 Bp ùTÚdLÜm UtßmYÏjRp Øû\«p Yô ódL êXjûRLôQXôm.
• GiLû[ ϱdLÜm ClT¥VôL YÏTÓmGiQôp ùTÚdLÜm.
ÁRm CÚkRôp, CûRúV §ÚmTÜm ùNnVÜm.
JÚ GiûQ AúR GiQôpùTÚd¡]ôp = YôódLm
number basic number Square =
ERôWQm
ôõùYh¥u ÏßdÏ ùYhÓ TWlT[Ü 3.46ùN.Á2. Õû[«u ®hPjûR LQd¸ÓùNnVÜm.
ôõùYh¥u ÏßdÏ ùYhÓ, Õû[«u ÏßdÏùYhÓdÏf NUm.
d1 þI LiÓ©¥dL
ùLôÓdLlThP TWlT[Ü = 3.46 cm2
TWlT[Ü = 0.785 x d2 (ãj§Wm)3.46 cm2 = d1
2 x 0.785
21mm (or) cm 2.1 d
cm 0.7853.46 d
0.785cm 3.46 d
22
=
=
=
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33
LôpÏúXhPûW TVuTÓj§ G°V LQdÏLs ùNnRp T«t£ 1.3.11
1 a .
b .
c .
d .
2 TWlT[Ü (A) = 2025ª.Á2
a = ª.Á
6 TWlT[Ü (A) =807.77 ùN.Á2
Es®hPm (d) =140 ª.Á
ùY° ®hPm (D)= ª.Á
3 T W l T [ Ü ( A ) =176.715 ª.Á2
d= ª.Á
4 TWlT[Ü (A) =65031 ª.Á2
£±V ®hPm (d) =140 ª.Á
ùTôõV ®hPm (D)= ª.Á
5 ¿[m (I) = 58 ùN.Á
ALXm (b) = 45ùN.Á
TWlT[Ü (A1)=TWlT[Ü (A2)
a = ùN.Á
7 TdLm (a) x TdLm(a) = 543169
TdLm (a) =ª.Á
8 d : l = 1:1.5
TWlT[Ü A = 73.5ª.Á2
d (®hPm) =__ª.Á
9 A§L¬dLlThPTWl×A = 12.7%
A = 360 mm2
d (®hPm) =__ª.Á
(d = A§L¬dLlThPT W l © ] ô pHtThP ®hPm)
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34
©RôLWv úRt\jûR TVuTÓj§ ùNnVlThP LQdÏLsT«t£ 1.3.12
1 TdLm ‘AC’- I Lôi AB = 15 ùNÁ, BC = 25ùNÁ.
AC2 = AB2 + BC2
= 152 + 252
= 225 + 625 = 850
AC = 850 = 29.155 cm
2 TdLm ‘BC’- I Lôi AB = 10 ùNÁ, AC = 30ùNÁ.
AC2 = AB2 + BC2
302 = 102 + BC2
900 = 100 + BC2
BC2 = 900 - 100 = 800
BC = 28.284 cm
3 TdLm ‘AB’- I Lôi BC = 20 ùNÁ, AC = 35ùNÁ.
AC2 = AB2 + BC2
352 = AB2 + 202
1225 = AB + 400
AB2 = 1225 - 400 = 825
AB = 28.72 cm
4 TdLm ‘BC’- «u U§lûTd Lôi AB = 8 ùNÁ,AC = 24 ùNÁ.
AC2 = AB2 + BC2
242 = 82 + BC2
576 = 64 + BC2
BC2 = 576 - 64 = 512
BC = 572 = 22.63 cm
5 TdLm ‘AC’- «u U§lûTd Lôi AB = 6.45ùNÁ, BC = 8.52 ùNÁ.
AC2 = AB2 + BC2
AC2 = 6.452 + 8.522
AC2 = 41.60 + 72.59
= 114.19
AC = 114.19 = 10.69 cm
6 TdLm ‘AB’- «u U§lûTd Lôi BC = 3.26ùNÁ, AC = 8.24 ùNÁ.
AC2 = AB2 + BC2
8.242= AB2 + 3.262
67.9 = AB + 10.63
AB2 = 67.9 - 10.63
= 57.27
AB = 57.27 = 7.57 cm
7 TdLm ‘AB’ - «u U§lûTd Lôi AC = 12.5ùNÁ, BC = 8.5 ùNÁ.
AC2 = AB2 + BC2
12.52 = AB2 + 8.52
156.25 = AB + 72.25
AB2 = 156.25 - 72.25
= 84
AB = 84 = 9.17 cm
§\]ônÜ T«t£ (Assignment)
• JÚ ùNeúLôQ ØdúLôQj§p TdLm AC =12.5 ùNÁ Utßm TdLm BC = 7.5 ùNÁ G²pTdLm ‘AB’ - u U§lûTd Lôi.
• JÚ ùNeúLôQ ØdúLôQj§p TdLm AB =6.5 ùNÁ Utßm TdLm BC = 4.5 ùNÁ G²pTdLm ‘AC’- u U§lûTd Lôi.
• JÚ ùNeúLôQ ØdúLôQj§p TdLm AC =14.5 ùNÁ Utßm TdLm AB = 10.5 ùNÁ G²pTdLm ‘BC’- u U§lûTd Lôi.
• JÚ ùNeúLôQ ØdúLôQj§p TdLm AB =7 ùNÁ Utßm TdLm BC = 5 ùNÁ G²pTdLm ‘AC’- u U§lûTd Lôi.
• JÚ ùNeúLôQ ØdúLôQj§p TdLm AC =13.25 ùNÁ Utßm TdLm AB = 8.75 ùNÁG²p TdLm ‘BC’- u U§lûTd Lôi.
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35
®¡Rm Utßm ®¡R NUm T«t£ 1.4.13
®¡Rm (Ratio)
A±ØLm
CWiÓ Wô£L°u Kôõ] A[ÜLû[Jl©ÓYRtÏ ®¡Rm Guß ùTVôó. CÕ©u]j§p ùY°lTÓjRlTÓ¡\Õ.
ùY°lTÓjÕRp (Expression)
a, b Gu\ CWiÓ Wô£Ls Kôõ] A[ÜLs
ùLôiPÕ. b
a ApXÕ a:b ApXÕ a ÷ b ApXÕ
a in b GuTÕ ®¡Rm
®¡Rm GlùTôÝÕm Ïû\kR GiL[ôLÏû\dLlTÓm
ERôWQm
®¡R NUm (Proportion)
CWiÓ ®¡ReLÞm NUUôL CÚdÏm, a : bGuTÕ ®¡Rm Utßm c: d GuTÕ Utù\ôÚ®¡Rm. CWiÓ ®¡ReLÞm NUm.
©\Ï,
a :b :: c : d or
ERôWQm
250 : 2000 :: 1 : 8
®¡R NUeL°uA¥lTûPLs (Proportionfundamentals)
G²p ©\Ï
• ad = bc
•
•
•c
dc
b
ba +=
+ Utßm
c
dc
a
ba +=
+
•
•
3:4::6:8 or
• 3 x 8 = 6 x 4
•
•
•
•
• 43
129
8 46 3
==++
• ®¡RmþCWiÓ Wô£L°u Kôõ]A[ÜLû[ Jl©ÓYÕ ®¡RmBÏm.
• ®¡R NUmþCWiÓ ®¡ReLÞmNUUôL CÚlTÕ ®¡RNUm BÏm.
ERôWQm
• 1:20 vúLÛdÏ, 800 x 1400 ª.Á G@Ï RLÓYûWVlTÓ¡\Õ. AkR RLh¥u ¿[mGqY[Ü? (TPmþ1)
Ïû\dLlThP ®¡Rm .
800 þp CÚkÕ Ïû\dLlThP B = 800 x = 40
ª.Á
Ïû\dLlThP ¿[m ( L) 1400 x = 70 ª.Á
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36
• ¡Vôó ¥WôuªNu²p, ùTôõV ¡Vôõp Es[TtL°u Gi¦dûL LiÓ©¥. (TPm 2)
úYLj§u ®¡Rm = 400 : 300
TtL°u ®¡Rm = 24:T
TtLs
A:B= 2:3 Utßm B:C=4:5 G²p A:B:C= _________ -- I LôiL,
A:B = 2:3
B:C = 4:5
A:B = 8 :12 (®¡Rm 2:3, 4- Bp ùTÚdLlThÓs[Õ.)
B:C = 12:15 (®¡Rm 4:5, 3 Bp ùTÚdLlThÓs[Õ.)
∴ A:B:C = 8:12:15
§\]ônÜ T«t£ (Assignment)
5 D : d = 1.75: 1ùTôõV ®hPm (D)= 35 ª.Á£±V ®hPm (d) =______ª.Á
6 a:s = 5:1
s = 1.5 ª.Á
a =______ ª.Á
7 A:B=9:12
B:C=8:10
G²p A:B:C=___________
8 A:B=5:6
B:C=3:4
G²p A:B:C= ___________
9 A:55=9:11
A = __________
10 15:9.3=40:x
x = ___________
1 l1 : l2 = 2:3¿[m (L) = 2.75ÁhPôóLsl1 = ______ÁhPôóLsl2 = ______ÁhPôóLs
2 `ôl¥u ®hPmd:`ôl¥u ¿[m(l)=2:7®hPm (d) = 40 ª.Á¿[m (L) = ______ª.Á
3 ® h P m : ¿ [ m(D:L)=1:10¿[m (L)=150 ª.Á®hPm (D) =______ª.Á
4
¿[m (l)=140ª.Áh = ________ ª.Á
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.4.13
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37
úSôó Uô\p Utßm G§ôó Uô\p T«t£ 1.4.14
®¡R NUm (Proportion)
®YWm (Description)
CWiÓ ®¡RØm JußdùLôuß NUUôLCÚdÏm, a:b GuTÕ JÚ ®¡Rm Utßm c:dGuTÕ Utù\ôÚ ®¡Rm. CWiÓ ®¡RØmNUUô]ûY. G²p
a : b::c : d ApXÕ ERôWQm 250 : 2000::1 : 8
êuß ®§Ls (Rule of three)
LQd¸Ó ùNnV êuß vùPlLs
• ®YWm (Statement)
• JÚYôó (Single)
• ùTÚdLp (Multiple)
G§ôóUô\p ApXÕ RûX ̧ r ®¡Rj§pUôßRp (Indirect or inverse proportion)
Ju±u A[Ü A§LôõdÏmùTôÝÕUtù\ôu±u A[Ü Ïû\Ùm. Ju±u A[ÜÏû\kRôp Utù\ôu±u A[Ü A§LôõdÏm.CÕ G§ôó Uô\p G]lTÓm. (TPm 2)
úSôó Uô\p (Direct proportion)
JÚ Wô£ JÚ ®¡Rj§p UôßmúTôÕ AúRôÓùRôPôó×ûPV Utù\ôÚ Wô£Ùm AúR®¡Rj§p UôßYúR úSôóUô\p G]lTÓm.(TPm 1)
ERôWQm
SôuÏ LûPNp ©¥lTYôóLs 300 ìTôn NmTô§d¡u\]ôó. CÕúY 6 LûPNp ©¥lTYôóLs GqY[Ü NmTô§lTôôóLs.
®YWm4 Pôó]ôóLs = ìTôn 300
JÚYôó
1 Pôó]ôó = ìTôn 75
ùTÚdLÜm 6 Pôó]ôóLs= 75 x 6 = 450 ìTôn
Ø¥Ü - A§LUô]ôp A§LôõdÏm
ERôWQm
SôuÏ Pôó]ôóLs JÚ úYûXûV 300 U¦úSWj§p Ø¥d¡u\]ôó CúR úYûXûV BßPôó]ôóLs ùNnÕ Ø¥dL GqY[Ü úSWmúRûYlTÓm?
êuß ¨ûXL°p ¾ôóÜ ùNnVlTÓm:
®YWm
4 Pôó]ôóLs GÓjÕdùLôiP úSWm = 300 U¦
JÚYo
1 Pôó]ôó GÓjÕd ùLôsÞm úSWm= 300 x 4 =1200 U¦úSWm
ùTÚdLÜm
6 turners = = 200 U¦úSWm
Ø¥Ü - A§LUô]ôp Ïû\Ùm
úSôóUô\p Utßm G§ôóUô\p CWiÓmLXkR LQdÏLs (Problem involving both)
ERôWQm
20 ÕiÓLû[ RVôôõdL CWiÓ Pôó]ôóLÞdÏêuß SôhLs úRûYlTÓ¡\Õ. BßPôó]ôóLs 30 ÕiÓLû[j RVôôõdL GjRû]SôhLs úRûY?
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38
ØR≠p BWm©lTÕ
2 Pôó]ôóLs, 20 ÕiÓLs = 3 SôhLs
6 Pôó]ôóLs, 30 ÕiÓLs = GjRû] SôhLsúRûY
ØRp vùPl (TPm 3)
®TWmPo]oLs 20 ÕiÓLs ùNnV = 3 SôhLs
1 Po]o 20 ÕiÓLs ùNnV = 3 x 2 = 6 SôhLs
6 Po]oLs 20 ÕiÓLs ùNnV ùTÚdÏL
= = 1 Sôs
G°ûUVô] ®¡RNUm (Simple proportion)
• ®¡RNUm
CWiÓ ®¡ReLÞdÏ CûPúVVô] NU¨ûXBÏm.
ERôWQeLs
• JÚ Yi¥ûV CVdL Sôs JußdÏ 30≠hPo ùThúWôp úRûYlTÓ¡\Õ. 6Yi¥Lû[ CúR ̈ ûX«p CVdL GqY[ÜùThúWôp úRûYlTÓm.
JÚ Yi¥dÏ TVuTÓj§V ùThúWôp = SôsJußdÏ 30 ≠hPoLs
CqYôß 6 Yi¥Ls TVuTÓj§]ôp =
BßUPeÏ úRûYlTÓm = 6 x 30 = 180 ≠hPo/Sôs.
• 4 Yi¥Ls CVeÏYRtÏ Sôs JußdÏ120 úLXu ùThúWôp úRûYlTÓ¡\Õ.CúR ̈ ûX«p 12 Yi¥Ls CVeÏYRtÏGqY[Ü úLXu ùThúWôp úRûYlTÓm.
4 Yi¥Ls JÚ Sôû[dÏ TVuTÓj§VùThúWôp 120 úLXu.
@ JÚ Yi¥ TVuTÓj§V ùThúWôp =
30 úLXu/Sôs.
@ 12 Yi¥Ls TVuTÓj§]ôp 12 x 30 = 360úLXu/Sôs.
CWiÓ ERôWQeLÞm G°ûUVô]®¡RNUm BÏm. Hù]u\ôp, CWiÓA[ÜLs UhÓúU TVuTÓjRlThPÕ Utßm CWiÓ ®¡Rj§ÛmSôhLs ùTôÕYôL Es[].
LXl× Utßm RûX ¸r ®¡R NUuLs(Compound and inverse proporions)
• LXl× ®¡R NUuLs.
ERôWQm
6 Yi¥Lû[ 5 ©hPoLs TÝÕ TôodL 21SôhLs ©¥jRÕ G²p 8 Yi¥Lû[ 7©hPoLs TÝÕ TôodL GjRû] SôhLsBÏm. (JqùYôÚ Yi¥dÏm TÝÕ TôodÏmúSWm ¨ûXVôL ùLôsL)
C§p úSoUô\p Utßm G§oUô\pTVuTÓjRlThÓs[Õ.
• JÚ ©hPo JÚ Yi¥ûV JÚ Sô°p TÝÕTôodL úRûYVô] úSWm. (Ïß¡V úSWm).
RûX¸r ®¡Rm -A§LUô]ôpÏû\Ùm.
CWiPôm vùPl (TPm 4)
®TWm: 6 Po]oLs 20 ÕiÓLs ùNnV = 1Sôs
JÚYo: 6 Po]oLs 1 ÕiÓ ùNnV =
Sôs
ùTÚdL: 6 Po]oLs 30 ÕiÓLs ùNnV= x 30 = 1.5 SôhLs.
úSo®¡Rm-A§LUô]ôp A§L¬dÏm.
LQdÏLû[ ¾oÜ ùNnV, ØR≠p®TWeLû[ GÝRÜm, ARu ©\ÏJÚYo Utßm ùTÚdLÜm,®¡ReL°u YûLûVl ùTôÚjÕ¾oUô²dLÜm.
A±ØLm
úUôhPôo YôL]eLÞdÏ LQd¸ÓùNnYRtLô] A¥lTûP ®¡RôNôWeLs ̧ úZ®Y¬dLlThÓs[Õ.
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.4.14
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39
• A[ÜLû[ (GjRû] SôhLs GuTÕ)LûP£«p GÓjÕd ùLôs[Xôm. Hù]²pAÕ ®ûPdLô] úRûYVôÏm.
®ûP; 7 ©hPoLs 8 Yi¥Lû[ 20 SôhL°pTÝÕTôolTôoLs.
SôhLs
RûX¸r ®¡Rm (Inverse proportion)
£X NUVeL°p ®¡ReLû[ RûX¸ZôL GÓdLúYi¥ CÚdÏm.
ERôWQeLs
• JÚ Tm×, G¬ùTôÚs ùRôh¥ûV ¨WlTGÓjÕdùLôsÞm úSWm 12 ¨ªPeLs.CÕúY CWiÓ Tm×Lû[ TVuTÓj§]ôpTô§ úSWj§p ¨WlTXôm.
úSWm CWiÓ UPeLôL BLd áPôÕ.
• CWiÓ Tml×Ls JÚ ùRôh¥ûV¨Wl×YRtÏ 30 ̈ ªPeLs úRûYlTÓ¡\Õ.CúR Uô§¬Vô] 6 Tm×Ls ùRôh¥ûV¨WlT GqY[Ü úSWm úRûYlTÓm.
®ûP ; 6 Tm×Ls GÓjÕdùLôiP
úSWm = ¨ªPm
G¬Rp NUuTôh¥p A[ÜL°u ®¡Rm(Proportional parts in combustion equation)
A±ØLm
A[ÜL°u ®¡Rm, G¬ùTôÚs G¬ÙmØû\dÏ JÚ Ød¡VUô] LôW¦VôÏm. G¬RpSûPùTßm ùTôÝÕ ¸rLiPûYLsSûPùTß¡u\].
G¬ùTôÚs ûahúWô LôoTu ùTôÚ[ôÏm.G¬YRtÏ úRûYVô] Lôtß Y° UiPXj§pCÚkÕ ¡ûPd¡u\Õ, A§p Bd£_u UtßmûShW_u Es[Õ. G¬ùTôÚs G¬ÙmùTôÝÕ ¸rLiP úY§«Vp Uôt\eLsHtTÓ¡u\].
• LôoTu Bd£_ú]ôÓ úNokÕ G¬ÙmùTôÝÕ Co Utßm Co2 BL Uôß¡\Õ.
(LôoTu úUô]dûNPôLÜm LôoTu ûPBdûNPôLÜm Uôß¡\Õ.)
• ûahW_u Bd£_ú]ôÓ G¬Ùm ùTôÝÕAÕ Ri¦WôL Uôß¡\Õ. (H2O)
• NpTo Bd£_ú]ôÓ G¬Ùm ùTôÝÕ AÕ
NpToûP BdûNPôL Uôß¡\Õ.
• ûShW_u JÚ UkRUô] YôÙ. AÕG¬YRtÏ ÕûQ ׬Y§pûX.
JÚ lb ùTôÚ°p Tϧ«u ®¡RjûRA±Ùm Øû\
ClùTôÝÕ LiÓ©¥dL úYi¥VÕ.
• JÚ lb/kg Ri½¬p Bd£_u UtßmûahW_u ®¡RjûR LôÔRp.
• JÚ lb/kg G¬ùTôÚ°p ûahW_u UtßmLôoT²u ®¡RjûR LôÔRp.
ERôWQeLs
• H2O. GuTÕ Ri½¬u úY§Vp ãj§WmBÏm. CRu ùTôÚs CWiÓ AÔdLsùLôiP ûahW_u Utßm JÚ AÔdLsùLôiP Bd£_²u LXûYLs úNokÕJÚ Uô≠dëp Ri½WôL Uôß¡\Õ.Bd£_u AÔ®u GûP ûahW_²uGûPûVl úTôp 16 UPeÏ A§LùU²pJÚ ¡úXô Ri½¬p ARu ®¡RjûRLiÓ©¥.
¾oÜ (Solution)
Ri½¬p TôLeL°u GûP ¸úZùLôÓdLlThÓs[Õ.
• Bd£_u = 16/2 = 8 ¡úXô
• ûahW_u = 1/1 = 1 ¡úXô
• ùUôjRm = 8+1= 9 ¡úXô
• ûahúWô LôoTu G¬ùTôÚ°u ãj§WmC6H14 BÏm. G¬ùTôÚ°u JÚ Uô≠dëp, 6LôoTu AÔdLs Utßm 14 ûahW_uAÔdLs Guß LôhÓ¡\Õ. ûahW_uAÔ GûPûVl úTôp LôoTu AÔ®uGûPVô]Õ 12 UPeÏ G²p, JÚ ¡úXôG¬ùTôÚ°p Es[ ûahW_u UtßmLôoTu ®¡RjûR LiÓ©¥.
¾oÜ (Solution)
LôoT²u TeÏ GûP«p = 6 x 12 = 72ûahW_u TeÏ GûP«p = 14.
ùUôjR TôLeLs = 72 + 14 = 86.
LôoT²u GûP = 72/86 = 0.8372 ¡úXô
ûahW_²u GûP 14/86 = 0.1628 ¡úXô
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.4.14
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40
®¡Rm Utßm ®¡RNUm
G¬YRtÏ úRûYVô] Lôt±u ®¡R A[Ü.
G¬ùTôÚs ØÝûUVôL G¬YRtÏ úRûYVô]Lôt±u ¨û\, ¸rLiP LôW¦Lû[lùTôÚjRÕ. CRtÏ Lôtß G¬ùTôÚs ®¡RmGuß ùTVo.
• – LôoTu, ûahW_u, NpTo B¡VûYBd£_àPu G¬dLlTÓ¡\Õ.
– G¬YRtÏ úRûYVô] Lôt±u A[ûY(GûP«p) LiÓ ©¥jÕ ARu êXmúRûYlTÓm A[®tÏ Bd£_uùNÛjÕlTÓ¡\Õ.
• – 1 ¡úXô LôoTu ØÝûUVôL G¬YRtÏ
= ¡úXô Bd£_u úRûY.
– 1 ¡úXô ûahW_u ØÝûUVôL G¬YRtÏ= 8 ¡úXô Bd£_u úRûY
– 1 ¡úXô NpTo ØÝûUVôL G¬YRtÏ = 1¡úXô Bd£_u úRûY.
• ØÝûUVôL G¬YRtÏ úRûYVô] ̈ û\ûVLiÓ©¥dÏm ãj§Wm
Lôt±p, Bd£_u 23% Utßm ûahW_u77% LXkÕs[Õ.
Lôt±u ̈ û\ = Bd£_u ̈ û\ x JqùYôÚêXlùTôÚÞm.
LôoTu ¡úXô Lôtß
ûahW_u 34.823
1008 =×= ¡úXô Lôtß
NpTo 4.3523
1001 =×= ¡úXô Lôtß
ùUôjRm(Total) 50.75 ¡úXô
CVk§Wj§p TVuTÓjÕm 1 ¡úXôG¬ùTôÚÞdÏ 50 .75 ¡úXô LôtßùNÛjRlTP úYiÓm.
G¬lTRtÏ 50.7 ¡úXô Lôtû\ ®PA§LUôL úRûYlTPôÕ.
LmTvPu NUuTôÓ LQdÏUôQYodÏ ªL A§LUô]A[YôÏm. Hù]²p C§púY§«Vp, CVt©Vp êXm TpúYßêXLeL°u ®¡RjûR LQd¸ÓùNnVúYiÓm.
§\]ônÜ T«t£ (Assignment)
1 ¿[m = 6.1 ÁhPoGûP = 32 kgfCúR Nô]≠u(channel) 1 ÁhPo¿ [ j § t L ô ]GûP = _______ kgf
2 £±V ®hPmd1 = 120 ªÁùT¬V ®hPmd2 = 720 ªÁ£±V ®hPj§un1 = 1200 rpmùT¬V ®hPj§un2 = ______ rpm
3 Z1 = 42 T
n1 = 96 rpm
n2 = 224 rpm
Z2 = _______ T
4 ám©u ®hPmD = 50 ªÁám©u EVWmH = 80 ªÁ¿ d L l T h Pám©u EVWmh = 36 ªÁ¿ d L l T h Pám©u ®hPmd = ______ ªÁ
5 JÚ ùUdLô²d 8 Gk§WeLû[ 3 SôhL°pANm©°e ùNn¡\ôo. 60 Gk§WeLû[ANm©°e ùNnYRtÏ GjRû] SôhLsBÏm.
6 BhúPô `ôl©p Es[ ¡ûWu¥e ÅpJÚ ¨ªPj§tÏ 1000 Ñtß Ñtß¡u\ÕUtßm ¥ûWYu ×p≠ (driven pulley)«u®hPm 200 ªÁ. ¥ûW®e ×p≠«u(drivingpulley) ®hPm 150 ¡.Á G²p ¥ûW®e×p≠«u rpm LiÓ©¥dLÜm.
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.4.14
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41
7 YôL]j§p ¡Vo AûUl©p ¸rLiPEiûULs LiÓ©¥dLlThP] 180 ªÁ®hPm Es[ ¡Vo 60 ªÁ ®hPm Es[¡VÚPu Cû]dLlThÓs[Õ. C§pùT¬V ¡Vo JÚ ¨ªPj§tÏ 60 ÑtßÑtß¡\Õ Gu\ôp. £±V ¡V¬u rpm ILiÓ ©¥..
8 JÚ YôL]m NmTkRlThP úYûXûV 5ùUdLô²dÏLs 4 SôhL°p Ø¥jÕ®hPôoLs G²p 3 ùUdLô²dÏLsGjRû] SôhL°p Ø¥lTôoLs.
9 JÚ YôL]j§p ¡VûW AûUdÏm ùTôÝÕTtL°u Gi¦dûL 26 ùLôiP ¡Vo 52TtLs ùLôiP ¡VÚPuCûQdLlTÓ¡\Õ. 52 TtLû[ ùLôiP¡V¬u ®hPm 200 ªÁ G²p 26 TtLû[ùLôiP ¡V¬u ®hPjûRLiÓ©¥dLÜm.
10 CWiÓ YôhPo Tm×Ls ùRôh¥ûV¨WlT 45 ̈ ªPm B¡\Õ. AúR Uô§¬Vô]4 YôhPo Tm×Ls TVu TÓj§]ôp,ùRôh¥«p Ri½ûW ¨WlT GqY[ÜúSWm BÏm.
11 ùTph ×p≠ CVdLj§p 12 ùN Á ®hPmEs[ ¥ûW®e ×p≠ JÚ ¨ªP§tÏ 360Ñtß Ñtß¡\Õ. G²p 20 ùN Á ®hPØs[¥ûWYu ×p≠«u rpm I LiÓ©¥
12 JÚ ¡Vo TôdûN TÝÕ TôolTRtÏ 12ùUdLô²dLÞdÏ 5 SôhLsúRûYlTÓ¡\Õ G²p B]ôp¡ûPdLdá¥V 7 ùUdLô²dÏLû[ ûYjÕTÝÕ TôodL GjRû] SôhLs BÏm.
13 ¸r LiPûYLÞdÏ NôRôWQ ®¡RmLôiL
a 45 ÷ 60 b 40 ûTNô ÷ ìTôn 4.00
c d 4°C ÷ 100°C
14 Lôtß 22% Bd£_u Utßm 78% ûShW_u¨û\ ùLôiPÕ. G¬ùTôÚs JÚ AXÏØÝûUVôL G¬YRtÏ úRûYVô] Lôt±uGûPûV LQd¸Ó ùNn. (G¬Y§pØd¡VUôL LôoTu, ûahW_u UtßmNpToLs TeÏ Y¡d¡\Õ).
ϱl×: ¸úZ úPhPô ùLôÓdLlThÓs[Õ(LQdûL ¾oÜ ùNn)
a 1 ¡úXô LôoTàdÏ úRûY 32
2 ¡úXô
Bd£_u.
b 1 ¡úXô ûahW_àdÏ úRûY 8 ¡úXôBd£_u.
c 1 ¡úXô NpTÚdÏ úRûY 1 ¡úXôBd£_u.
15 ûa¥úWô LôoTu G¬ùTôÚ°uêXôRôWm C7H14. CkR G¬ùTôÚ°uJqùYôÚ Uô≠dë≠p, 7 AÔ LôoTàm,Utßm 19 AÔ ûahW_àm CÚdÏm.C§p LôoTu AÔ®u GûP ûahW_uAÔûY ®P 12 UPeÏ A§Lm G²p JÚ¡úXô G¬ùTôÚ°p CÚkÕ ûahW_uUtßm LôoT²u ®¡RjûR LiÓ©¥.
16 ìTôn 20,000/ U§l× EûPV YôL]m, AÕì 150/ dÏ LôlÀÓ ùNnVlThÓs[Õ. CúRA¥lûP«p 24,000/ ìTôn U§l×s[YôL]jûR 1 YÚPm 3 UôRj§tÏ LôlÀÓùNnRôp LôlÀÓ ùRôûL GqY[ÜCÚdÏm. (LômTÜiÓ ®¡Rm).
20 ª.Á
4 ÁhPo
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.4.14
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42
NRÅRm T«t£ 1.5.15
NRÅRm (Percentage)
NRÅRm GuTÕ JÚ YûLVô] ©u]m. CRuTϧ GlùTôÝÕm 100 BL CÚdÏmNRÅRj§u ϱÂÓ% Gi¦tÏ ©\ÏCdϱûV TVuTÓjR úYiÓm. ERôWQUôL
= 16%.
CÕ RNU Y¥Yj§p, 0.16. NRÅRd LQd¸Ómêuß ®§Lû[ Es[Pd¡VÕùLôÓdLlThP úPhPô, AXÏ, Utßm ©\ÏùTÚdÏRp CÕRôu ®ûP LôÔYRtLô]LQd¸Ó Øû\VôÏm. (TPm 1)
Ø¥Ü
C§p TVuTÓjRlThP êuß vùPlLs
ØRp vùPl: ãr¨ûXûV ®[dÏRp(CÚlTûR ûYjÕ ùNnYÕ)
CWiPôm vùPl: AXÏLû[ Ø¥Ü ùNn
êu\ôm vùPl: ùTÚdLp BWm©dLÜm.
ùLôÓdLlThP úPhPôûYTÏjRônÜ ùNnÕ, ®ûPûV AXÏêXUôL LiÓ©¥dLÜm.
ERôWQm (Example)
JÚ ©hPo ©¥jRmúTôL Åh¥tÏ GÓjÕfùNpÛm UôRNmT[m ì 984.50 AYÚûPVNmT[j§p 24%, ©¥jRm ùNnVlTÓ¡\ÕG²p AYÚûPV ùUôjR NmT[m GqY[Ü?(TPm 3)
ERôWQm (Examples)
JÚ v¼p LRÜ RVô¬dL 3.6 N.ÁhPo CÓùTôÚs úRûYlTÓ¡\Õ Utßm C§pHtTÓm úNRôWm 0.18 N.ÁhPo G²púNRôWj§u NRÅR U§l©û] (TPm 2)LiÓ©¥.
êuß vùPl êXm ¾ôóÜ LôQlTÓ¡\Õ
vúPhùUih: (Statement)
LR®u TWlT[Ü (A) = 3.6 Á2 = 100 %.
úNRôWm = 0.18 Á2
JÚYo: 3.6100
1 Á2
ùTÚdLp: for 0.18 Á2= 3.6100
x 0.18.
L¯Ü = 5%.
ùUôjR NmT[m 100%
©¥jRm 24%
ÅhÓdÏ GÓjÕf ùNpÛm NmT[m 76%
100 ìTôn NmT[j§p AYôó ÅhÓdÏ GÓjÕfùNpÛm NmT[m ìTôn 76
JÚ NR®¡Rj§tÏ 76
1
ìTôn 984.50, it is 76
1 x 984.50.
@100 dÏ 1295.39X10076
984.50=
100%ARôYÕ, ùUôjR NmT[m = ìTôn 1295.40.
ERôWQm 1 (Example 1)
200 ≠hPo ùLôs[[Ü ùLôiP úTW≠pCÚkÕ 75 ≠hPôó GiùQn ùY°úVGÓdLlTÓ¡\Õ G²p ùY°úV GÓjRGiùQn«u NR®¡RjûR LiÓ©¥.
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43
¾ôóÜ
GÓdLlThP GiùQn«u NR®¡Rm =ùY°«p GÓdLlThP GiùQn (≠hPôõp)/ úTWp ùLôs[[Ü (≠hPôóv) x 100
ERôWQm 2 (Example 2)
15000/- ìTôndÏ E§¬ TôLm 15% XôTj§tÏYô¥dûLVô[ÚdÏ ®tLlTÓ¡\Õ G²p.¸rLiPYtû\ LiÓ©¥ (a) Yôe¡V ®ûXGu] (b) GqY[Ü XôTm. .
¾ôóÜ: ùTôÚ°u ®ûX (CP) = x ,
ùTôÚ°u ®ûX (CP) = cost price
®t\ ®ûX (SP) = sale price
®t\ ®ûX=ùTôÚ°u ®ûX+®t\®ûX«p15%
15000= +
XôTm = ®t\ ®ûX-ùTôÚ°u ®ûX = 15000-13043=1956.53
Yôe¡V ®ûX= Rs.13,043/,XôTm = Rs. 1957/
ERôWQm 3 (Example 3)
ùUôjRm 80000 Lôô óLû[ ŧ«púNô§jRùTôÝÕ, A§p 16000 LôôóLs Gq®RÏû\LÞm CpXôUp CÚkRÕ G²pHtßdùLôs[lThP LôôóL°u NR®¡RmGqY[Üþ
=
ERôWQm 4 (Example 4)
úUôhPôôó ûNdLõs ®ûX 92% A[®tÏÏû\kÕ®hPÕ. AÕ RtùTôÝÕ ì 18000/-dÏ ®tTû] ùNnVlTÓ¡\Õ G²p ARuEiûUVô] ®ûX Gu].?
¾ôóÜ
RtùTôÝÕ úUôhPôôó ûNdL¡s ®ûXì. 18000/-
EiûUVô] ®ûX«p CRu U§l× 92% BÏm.
EiûUVô] ®ûX= 18000 x
= Rs.19565/-
ERôWQm 5 (E(E(E(E(Example 5)xample 5)xample 5)xample 5)xample 5)
JÚ úUôhPôôó YôL]m, JÚ U¦ úSWj§p 30¡úXô ÁhPôó úYLj§p ùNu\ôp 100 ≠hPôóùThúWôp ùNXYô¡\Õ. YôL]jûR TÝÕTôôójR ©u JÚ Sôû[dÏ 90 ≠hPWôLÏû\kÕ®hPÕ. G²p úNªlûTNR®¡Rj§p LQd¡Ó.
¾ôóÜ
úNªl× NR®¡Rj§p= Ïû\kR ÖLôóÜ/BWmTÖLôóÜ x 100
= (100 – 90) x100
=
= 10% GôõùTôÚs ªfNm
§\]ônÜ T«t£ (Assignment)
1 NÕWj§u TdLm =400mm (side of square)
®hPm = 400 ª.Á
L¯Ü = ______ %.
2 ®hPm (d) = 26ª.Á
ùYhÓ BZm ('a')depth of u/cut = 2.4ª.Á Ï ß d Ïù Y h Óú R ô t \ j § pT W l T [ Ü= ______ %
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.5.15
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3 A§LôõdLlThPNR®¡Rm = 36%
A§LôõdLlThPU§l×
= 611.2 ¨ëhPuªÁ2
E i û U V ô ]CÝ®ûN=_____ ¨ëhPu/ª.Á2.
4 AXô«p Es[ùNm×= 27 ¡úXô
AXô«p Es[ÕjRSôLm = 18¡úXô
ùNm©u NRÅRm= ________%% ÕjR SôLj§uNR®§m = ______%.
5 AXô«u GûP= 140 KgfSn GûP = 40%Pb = ______ KgfSn = ______ Kgf.
6 ú`PhTϧ = ______ %.
7 A Ý j R l T h P¿[m = ______ %.
8 ®hPm (d) = 360 mm
TdLm (a) = 0.707 x d
L¯Ü = ______ %.
9 Cu = 36 ¡¡
Zn = 24 ¡¡
Cu = ______ %
Zn = ______ %
10 Cu = 42.3 ¡¡
Sn = 2.7 ¡¡
Cu ______ %
Sn = ______ %.
11 JÚ E§¬ TôLm ì.195/- dÏ YôeLlTÓ¡\Õ.CÕ ®tTû] YõûX«p 65% G²p ®tTû]®ûX GqY[Ü.
12 JÚ úUôhPôôó ûNd¡s PVôó ìTôn 300þdÏ ®tLlTÓ¡\Õ. C§p 25% XôTmúNodLlTh¥ÚkRôp. CRu Yôe¡V ®ûXGqY[Ü.
13 Lôt±p 23% Bd³_u Utßm 77%ûShW_àm CÚkRôp 120 L] ÁhPôóLôt±p GjRû] L]ÁhPôó êXLeLsEs[]?
14 JÚ ¼Np Gu£u úTôõe A[®p Es[êXlùTôÚhLs ¸úZ ùLôÓdLlThÓs[].
a) ùNm× (Cu) - 86%
b) ùYsÇVm (Sn) - 10%
c) ÕjR SôLm (Zn) - 4%
AXô«u GûP 40 ¡úXô BÏm. C§pJqùYôÚ êXLeL°u GûPûV LôiL.
15 BhúPô ôõlúTôó ùNnÙm úLúW_õpúNôpPôó TVuTÓjRlTÓ¡\Õ. A§p 35%ùYsÇVm Utßm 65% DVØm LXkÕEs[Õ. úNôXóPôõu GûP 40 ¡úXô Gu\ôpêXLeL°u GûPûV R²jR²úVLiÓ©¥dLÜm.
16 Lôôõp 4 ®RUô] TVQm ùNnVlTÓ¡\Õ.JqùYôÚ TVQj§u çWm 200 ûUpLsCkR SôuÏ TVQeL°Ûm ùThúWôpETúVôLm Øû\úV 6.65, 7.5, 6.85, Utßm7.05 úLXuLs BÏm.
¸úZ Es[ûYLû[ LiÓ©¥:
1 JqùYôÚ TVQj§u úTôÕm NWôNôõùThúWôp TVuTôÓ
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.5.15
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2 JqùYôÚ ûUÛdÏm ùNXYô] NWôNôõùThúWôp
3 TVuTÓjRlThP NWôNôõ ùThúWôpNRÅRj§u A¥lTûP«p A§LUôLTVuTÓjRlThP ùThúWôûXNR®¡Rj§p á\Üm. CûR NôõVôLCWiÓ RNUj§tÏ LiÓ©¥dLÜm.
17 úTôdÏYWjÕ T¦Uû]«p, ØRÄhÓYÚUô]j§p ¸rLiP ùNXÜLsLiÓ©¥dLlThPÕ.
1 PVÚdLôL 40% YÚUô]mùNXY¯dLlThPÕ
2 GôõùTôÚs Utßm EVÜl ùTôÚÞdLôL30% YÚUô]m ùNXY¯dLlThPÕ
3 E§¬ TôLeLÞdLô] ùNXÜ 10%.
UôR Ø¥®p ì 2000/- úNªdLlTÓ¡\ÕGu\ôp ùUôjR YÚUô]m GqY[Ü.
18 JÚ Lôv¥e¡u GûP 80 ¡úXô¡Wôm.BWmTLhP ùU£²e¡p ARu GûP 4%Ïû\¡\Õ Ut\m CߧLhP ùU£²e¡p5% GûP Ïû\¡\Õ G²p, ùU£²eùNnVlThP TôLj§u Cߧ GûPGu]YôL CÚdÏm.
19 25 ¡úXô¡Wôm GûPÙs[ Lôv¥e¡pÕjRSôLm 35% ùNm× 40% Utßm 25%ùYsÇVm CÚkRôp, R²jR²úVAYt±u GûP Gu]YôL CÚdÏm.
20 JÚ NôpP¬p 35% ùYsÇVm 65%. LôÃVmEs[Õ, C§p ùYsÇVj§u GûP 14¡Wôm G²p, NôpP¬u ùUôjR GûPGqY[Ü.
21 JÚ úNpvúUu UôR NmT[m ì 1000/--Utßm 2.5% úNpv Lª`]ôL ùTß¡\ôo.AYo JÚ YÚPj§p ì. 60,000/= -U§l©tÏúNpv ùNnÕ ùLôÓjRôp AY¬u ùUôjRYÚUô]m Gu]YôL CÚdÏm.
22 JÚ U²Ru Ru YÚUô]j§p 15%®YNôVj§tÏm, 21% ÏÓmTj§tÏm, 24%ÏZkûRLs Lp®dÏm Utßm úNªlTôLì 360/= ûL«p ûYj§ÚkRôp AY¬u UôRùUôjR YÚUô]m GqY[Ü?
23 JÚ U²Ru Rôu YôeÏm UôR YÚUô]mì 450/= p ì 90/= I úNªjÕ ûYjRôp,AY¬u úNªl× GjRû] NRÅRm CÚdÏm.
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.5.15
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46
NRÅRj§≠ÚkÕ RNU©u]m Utßm NôRôWQ ©u]UôL UôtßRpT«t£ 1.5.16
NôRôWQ ©u]jûR NRÅRUôL UôtßRp.
1 NRÅRUôL UôtßL
¾oÜ: x 100
= 50%
2 111----- - -I NRÅRUôL UôtßL
¾oÜ: 111
x 100 = 11100
= 9.01%
¸rYÚm NôRôWQ ©u]eLû[ NRÅRUôLUôtßL.
1 41
2 51
3 32
4 83
NRÅRjûR NôRôWQ ©u]UôL UôtßRp.
1 24% -I NôRôWQ ©u]UôL UôtßL
¾oÜ: 10024
= 256
2 3133 % -I NôRôWQ ©u]UôL UôtßL
¾oÜ: 100
3133
= 100
13
100 100
3100
×=
= 31
¸rYÚm NRÅRjûR NôRôWQ ©u]UôLUôtßL.
1 15%
2 %2187
3 80%
4 125%
RNU©u]jûR NRÅRUôL UôtßRp.
1 0.35 - I NRÅRUôL UôtßL
¾oÜ: 0.35 x 100
= 35%
2 0.375 - I NRÅRUôL UôtßL
¾oÜ: 0.375 x 100
= 37.5%
¸rYÚm RNU©u]eLû[ NRÅRUôLUôtßL.
1 0.2
2 0.004
3 0.875
4 0.052
NRÅRjûR RNU©u]UôL UôtßRp.
1 30% - I RNU©u]UôL UôtßL
¾oÜ: 10030
= 0.3
2 %3133 - I RNU©u]UôL UôtßL
¾oÜ: 100
3133
= 100
13
100 100
3100
×=
= 31
= 0.333
¸rYÚm NRÅRjûR RNU©u]UôLUôtßL.
1 15%
2 7%
3 %2112
4 90%
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47
CVtL¦Rd ϱÂÓLs Utßm A¥lTûPLs T«t£ 1.6.17
A±ØLm (Introduction)
ùR¬VôR GiL°u U§lûT ùR¬kÕ ùLôs[úYi¥V CPj§p, CVtL¦Rj§p,GÝjÕdLs TVuTÓjRlTÓ¡\Õ. CÕ JÚYûL L¦RUôÏm. CqYûL LQd¡p,GÝjÕdLÞPu GiLÞm úRûYlTÓmCPeL°p U§l©tÏ HtT TVuTÓjRlTÓ¡u\]. ERôWQj§tÏ 3X Utßm X3,CWi¥Ûm X þu CPm ®j§VôNlTÓ¡\Õ.3X þp 3 Gu\ Gi X þBp ùTÚdLlThÓs[Õ.B]ôp X3 þp 3 Gu\ Gi Xþu Index BLEs[Õ.
Tô£¥q Utßm ùSL¥q GiLs (Positiveand negative numbers)
Tô£¥q GiLÞdÏ Øu]ôp + ϱÂÓmUtßm ùSL¥q GiLÞdÏ Øu]ôp þϱÂÓm ϱdLlTÓm. CúR Øû\ûVGÝjÕdLÞdÏm SûPØû\TÓjRlTÓ¡\Õ.
ERôWQm (Example)
+ X, - Y
+8 (A) 8 Guß Tô£¥q GiûQd ϱdLXôm.
þ8 GuTÕ ùSL¥q GiQôÏm.
áhPp Utßm L¯jRp (Addition and subtrac-tion)
CWiÓ Tô£¥q GiLû[ áhÓm úTôÕ,ARu A[ÜLs áh¥, ARu Øu×\j§páhPp ϱûV ϱdL úYiÓm.
CWiÓ ùSL¥q GiLû[ áhÓm úTôÕ,ARu A[ÜLs áh¥, Øu×\j§p L¯jRpϱûV ϱdL úYiÓm.
Tô£¥q Utßm ùSL¥q GiLû[ áhÓmúTôÕ ARu A[ÜL°u ®j§VôNjûRϱdL úYiÓm. úUÛm C§p GkR A[ÜùT¬VRôL Es[úRô ARu ϱÂhûP ØuTdLm ϱdL úYiÓm.
+ 7+ 22 = + 29
- 8 -34 = -42
- 27 + 19 = - 8
44 + (-18) = +26
37 + (-52) = (-15)
Tô£¥q Utßm ùSL¥q GiLû[ùTÚdÏRp (Mulitiplication of positive andnegative numbers)
JúW ϱÂÓ Es[ CWiÓ Tô£¥q GiLû[ùTÚd¡]ôp ARu ùTÚdÏj ùRôûLûV +ϱÂhPôp ϱdL úYiÓm. LY²dL,CWiÓ ùTÚdÏ GiLÞm ùSL¥q BLCÚkRôp ARu ùTÚdÏ ùRôûL + Tô£¥qBÏm.
ERôWQm (Example)
– 20 x –3 = 60
5 x 8 = 40
4 x –13 = –52
–5 x 12 = –60
YÏjRp (Division)
YÏTÓm Gi YÏdLlTÓm GiQôpYÏdLlTÓ¡\Õ. CqYôß YÏjRôp YÚm®ûP DÜ G]lTÓ¡\Õ. YÏTÓm GiÔmYÏdLlTÓm GiÔm JúW ϱÂhPôLCÚkRôp, DÜ + áhPp ϱVôÏm. ùYqúYßϱÂÓLs CÚkRôp ARu ®ûPûV þ ùSL¥qϱÂPôL ϱdL úYiÓm.
JÚ LQd¡p áhPp, L¯jRp,ùTÚdLp, Utßm YÏjRp CÚkRôpØR≠p ùTÚdLp Utßm YÏjRÛmARu ©\Ï áhPp Utßm L¯jRÛmùNnV úYiÓm.
ERôWQm (Example)
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48
AûPl×dϱLs Utßm ϱÂh¥uùRôϧ (Parenthesis and grouping symbols)
( ) ©WôdLh (Brackets)
{ } ©úWNv (Braces)
7 + (6 - 2) = =4 = 11
6 X (8 - 5) = 6 X 3 =18
AûPl×dϱLs (Parenthesis)
CkR YûL ϱÂÓLs £X áhPp UtßmL¯jRûX, ùTÚdLp Utßm YÏjRÛdÏØu]ôp ùNnV úYiÓm. Á§ úYûXLû[ùNnYRtÏ Øu CRtÏs Es[ ϱl©hPúYûXLû[ ØÝûUVôL Ø¥dL úYiÓm.ϱÂh¥u ùRôϧ Ø¥kR ©\Ï, ϱÂÓLû[¿dLÜm.
ϱÂh¥u ùRôϧûV EP]¥VôL ØuTdLmϱdL úYiÓm. (A) GiLÞdÏ Øu]ôpϱdL úYiÓm. B]ôp ϱÂÓCpûXùV²p Sôm ùNnV úYi¥V ®`VmùTÚdLp GuTûRd ׬kÕ ùLôs[ úYiÓm.
L¯jRp Utßm ùSL¥q GiLû[ ùTÚdLpùNnÙm ùTôÝÕ Ï±Âh¥u ùRôϧûVTVuTÓjR úYiÓm.
ùSL¥q ϱÂÓ Øu]ôp Es[ ϱÂh¥uùRôϧûV ¿dÏm úTôÕ, ϱÂh¥uùRôϧ«p Es[ GpXô ϱÂÓLû[ÙmUôt\ úYiÓm. (+ ϱÂh¥p CÚkÕ þϱÂhÓdÏm Utßm þ ϱÂh¥p CÚkÕ +ϱÂhÓdÏm Uôt\ úYiÓm.)
AûPl×d ϱLs Øu + ϱÂÓ CÚkRôpϱÂÓL°u úLôûYLû[ Uôt\ôUp +ϱÂÓLû[ ¿dLXôm.
ϱÂh¥u JÚ ùRôϧ Utù\ôÚùRôϧÙPu ùTôÚk§ CÚkRôp, ØRpùNh¥u ªLÜm AÚ¡p Es[ûR ¿dLúYiÓm.
ùTôÕYô] A[ÜLs + ApXÕ þ ϱÂh¥uêXm CûQdLlTh¥ÚkRôp CkRùTôÕYô] A[Ü AûPl×d ϱdÏ ØuTôLûYdL úYiÓm.
8 + 6 (4-1) = 8 + 6 X 3 =36
(6+2) (9 -5) = 8 X 4 =32
áhPp + 4, ùSL¥q þ 7 CûR 4 þ (þ 7) GußGÝR úYiÓm.
áhPp + 4, - - I 7 Bp ùTÚdL 4(-7) Guß GÝRúYiÓm.
4 - (-7) = 4+7 =11
8 - (7 -4) = 8 - 3 = 5
3 + (- 8) = 3 - 8 = -5
7 + (4 - 19) = 7 + (-15) = 7 - 15 = - 8
3 {40+ (7 +5) (8 - 2)} =3 {40+12 X 6} = 3 X 112 = 336
8x + 12 C§p 4 þI LôW¦VôL TVuTÓj§]ôp
8x + 12 GuTÕ 4 (2x +3) G]lTÓm.
EhTϧ«Ûs[ ϱÂh¥u ùRôϧûVØR≠p ÑÚdL úYiÓm.
CVtL¦R ϱÂÓLs Utßm JÚ T¥fNUuTôÓLs (Algebric symbols and simple equa-tions)
CVtL¦R ϱÂÓLs (Algebric symbols)
ùR¬VôR GiL°u U§l× GÝjÕdLs êXmϱdLlTÓ¡\Õ. CÕ CVtL¦R ϱÂPôÏm.
LôW¦ (Factor)
LôW¦ GuTÕ GiLs (A) GÝjÕdLs (A)ùRôϧ BÏm. HRôYÕ Ju\ôL CÚdLXôm.AûY ùTÚdÏm úTôÕ ¡ûPdL á¥VûY
Gdv©W`u (expression) BÏm. 12þu LôW¦Ls
4 Utßm 3 (A) 6 Utßm 2 (A) 12 Utßm 1.
8x+12 Gu\ Gdvl©W`û] CqYôßLôW¦TÓj§ GÝRXôm.
4 (2x + 3), 4 Utßm (2x + 3) LôW¦Ls BÏm.
CVtL¦R úLôûYLs (Algebris terms)
JÚ Gdv©W`²p CWiÓ ApXÕCWiÓdÏ úUtThP TϧLs R²jR²VôLCÚkRôp ARôYÕ + (A) þ, JqùYôÚ TϧÙmúLôûYLs G]lTÓm.
Y - 5x GuTÕ GdvlW`]ôÏm, Y Utßm - 5xGuTÕ úLôûYLs BÏm.
úLôûYLÞdÏ Øu]ôp ϱÂÓ Ï±dLúYiÓm.
ÏQLm (Co-efficient)
JÚ GdvlW`u LôW¦L[ôL AûUdLlùTt\ôp ARu ùTÚdÏj ùRôûLGdvlW`u BÏm. ©\Ï JqùYôÚ LôW¦ÙmÁRØs[ LôW¦L°u ÏQLm BÏm.
12x þu ÏQLm 4 BÏm.
48 þu ÏQLm x BÏm.
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.6.17
© NIMI, Not to be republished
49
NUuTôÓ (Equation)
CWiÓ GiLÞdÏ CûPúVVô] NU¨ûX(A) GiLs Ut\m CVtL¦j ϱÂÓLsNUUôL CÚl©u CÕ NUuTôÓ G]lTÓm.
JÚ T¥f NUuTôÓ (Simple Equation)
ØRp AÓd¡u (Power) CVtL¦R ϱÂÓPuCÚkRôp AÕ JÚ T¥fNUuTôÓ G]lTÓm.
áhPp Utßm L¯jRp (Addition and subtrac-tion)
JúW ϱÂÓ Utßm AÓdÏLs (power)ùLôiP úLôûYLs BL CVtL¦RϱÂhÓPu Gi¦dûL CÚkRôp áhPpUtßm L¯jRp ùNnVXôm.
10x + 14 – 7y2 – 11a + 2x – 4 – 3y2 – 4a + 8
= 10x + 2x – 7y2 – 3y2 – 11a – 4a + 14 – 4 + 8
= 12x – 10y2 – 15a + 18
2x = 10, 2x + 6 = 10 + 6
y + 12 = 20, y + 12 – 8 = 20 – 8
x + 10 = 12,
x + 10 – 10 = 12 – 10
3x = 6, 2 x 3x = 2 x 6, 6 x = 12
5y = 20, 5
20 =
5
5y
NUuTôhûP UôßRp ùNnVôUp JúWYûLVô] GiLû[ áhPXôm UtßmL¯dLXôm.
NUuTôh¥u JqùYôÚ Eßl×Lû[Ùm AúRGiL[ôp ùTÚdLúYô (A) YÏdLúYôùNnVXôm. (NUuTôh¥u NU¨ûXjRuûUûV Uôt\ôUp).
GiLs ApXÕ Ï±ÂÓLû[ CWiÓ TdLØmáhÓRp (A) L¯jRp ùNnÙm úTôÕNUuTôh¥u NU¨ûX Uô\ôÕ. AúRúTôpùTÚdLp Utßm YÏjRp ùNnÙm úTôÕAúR GiLs (A) ϱÂÓLs CWiÓ TdLØmùNnÙm ùTôÝÕ NU¨ûXj RuûUûVTô§dLôÕ.
JÚ T¥ NUuTôh¥p úLôûYL°u Y¬ûNUôßTÓm úTôÕ (Transposition of the terms ofthe equations)
= NUm
+ áhPp
þ L¯jRp
X ùTÚdLp
YÏjRp
NUuTôh¥u RjÕYm (Concept of equality)(TPm 1)
NUuTôhûP JÚ _ûR vúLÛPu Jl©ÓmúTôÕ, CûY GlúTôÕm NUUôL CÚdÏm.CÚ TdLØm Es[ NUuTôhûP Uôt±AûUjRôÛm NUUôLúY CÚdÏm. 9 = 5 + xGuTûR 5+x = 9 Gußm GÝRXôm.
CÚ TdLØm Es[ NUu TôhûP CúRØû\«p ùNnÕ NUuTÓjR úYiÓm. JúWU§lûT CWiÓ TdLØm áhPúYô (A)L¯dLúYô ùNnVXôm. 5+ x = 9 EPu CÚTdLØm 3þI áhPÜm. CqYôß ùNnRôp, 5+x+ 3 = 9 + 3 (A) X+8 =12 BL NUuTôÓ B¡®Óm.5 + x = 9 C§≠ÚkÕ 5þI CWiÓ TdLØmL¯dLÜm. ©\Ï 5+ x - 5 = 9 -5. x =4.
5þI CPÕ Utßm YXÕ TdLm Uôt±AûUjRôp ϱÂÓLû[ + p CÚkÕ þ dÏUôt\Üm.
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.6.17
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4
x = 20 CWiÓ TdLØm 4 þ Bp ùTÚdLÜm.
©\Ï 4
x x 4 = 20 x 4.
X = 80
5x = 25
CWiÓ TdLØm 5 þBp YÏdLÜm
©\Ï 5
25 =
5
5x = x = 5
GiLs ApXÕ Ï±ÂÓ GÝjÕLs JÚTdLj§≠ÚkÕ AÓjR TdLm Uô±]ôp,ùTÚdLp YÏjRXôÏm, YÏjRpùTÚdLXôLÜm Uôßm.
CWiÓ TdLØm Es[ NUuTôhûPNUUôL LÚ§ ùNVpTÓm ùTôÝÕNUuTôh¥u NU¨ûXUôßTÓY§pûX.
JÚ TdLj§≠ÚkÕ Utù\ôÚTdLj§tÏ Uôt\lThPôp áhPpA[Ü L¯jRp A[YôL Uôß¡u\Õ.
L¯jRp A[Ü áhPp A[YôLUôß¡u\Õ.
ùTÚdLp YÏjRXôL Uôß¡u\Õ.
YÏjRp ùTÚdLXôL Uôß¡u\Õ.
JÚ T¥f NUuTôh¥u ¾oÜLôQAf NUuTôh¥u CPÕ TdLmùR¬VôR GiL°u U§lûTR²ûUlTÓjÕYRu êXm G°VNUu Tôh¥tÏ ¾oÜ Ø¥Ùm.
ERôWQm (Example)
¾oÜ LôiL.
4x = 3(35 – x ) Gu\ôp x þu U§lûT LôiL.
4x = 105 – 3x (AûPl× Ï± ¿dLlThÓ®hPÕ)
4x + 3x = 105 (-3x þI YXÕ ×\j§p CÚkÕCPÕ ×\j§tÏ UôtßL)
7x = 105
x = 15 (CWiÓ TdLØm 7 Bp YÏdLÜm).
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.6.17
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CVtL¦Rj§p Es[ ©¬Yô] áhPp, L¯jRp, ùTÚdLp UtßmYÏjRp T«t£ 1.6.18
áhPp
ERôWQm 1
áhÓL 2x, 3x, 7x
¾oÜ : C§p ùYßm áhPp UhÓmCÚlTR]ôp JqùYôÚ AûPl×dÏsÞm ‘+’ϱÂÓ ùNnVÜm.
= (+2x) + (+3x) + (+7x) = 12x
áhÓL
-3a, -2a, -5a
= (-3a) + (-2a) + (-5a) = -10a
ERôWQm 2
áhÓL 10xy, -8x2, -7xy, -7x2
= (10xy) + (-8x2) + (-7xy) + (-7x2)
= (10xy) + (-7xy) + (-8x2) + (-7x2)
= (3xy) + (-15x2)
ERôWQm 3
áhÓL 8a
,2a
,4a
−
L¯jRp
ERôWQm 1
2 ÁhP≠ÚkÕ 8 ÁhPûW L¯dLÜm
¾oÜ : (2m) - (8m)
+8 -≠ÚkÕ L¯dL úYiÓm Uôt±V©u + 2m ϱÂÓ - 8m
áh¥V©u - 6m
ERôWQm 2
L¯jRp (-5x + 3y) from (7x + 8y)
¾oÜ: (7x + 8y) - (-5x + 3y)
+ 7x + 8y
+ 5x - 3y
+ 12x + 5y
‘-’ ϱÂhÓPu Es[ Aû]jÕ úLôûYLû[Ùm (terms) ùTÚdLÜm. ARàPu áhPpUtßm L¯jRp ùNnV úYi¥V úLôûYLû[¸úZ ùNôp≠V vùPl£uT¥ ùNnVÜm.
G°V NUuTôÓLÞdÏ ¾oÜ LôÔRp
CVtL¦R ϱÂh¥tLô] E\Ü ®§Ls
1 ùTÚdLp ®§Ls
(i) + x + = +
(ii) - x - = +
(iii) + x - = -
(iv) - x + = -
2 YÏjRp ®§Ls
(i)
(ii) +=−−
(iii) −=−
+
(iv) −=+−
ERôWQeLs
1) a + 4 = 7
a = 7 - 4
a = 3
2) M - 5 = 3
m = 3 + 5
m = 8
3) 7P = 17
P = 7
17
4)6x
= 9
x = 9 x 6
x = 54
5) 7x + 3 = 15 + x
7x -x = 15 - 3
6x = 12
© NIMI, Not to be republished
52
x = 6
12= 2
6) 0y9
5=
Y = 0 x 5
9
y = 0
45
810M
852XM
2M58
68M58
86M58
==
=
=
−=
=+7)
36x
365
6 x 30x
6 x 305x
306
3x 2x
302
x
3
x
=
==
=
=+
=+8)
1443
12 x36x
36123x
3612
2x -5x -4x 6x
36 6x
125x
3
x
2
x
36 6x
125x
3
x
2
x
==
=
=+
=−−+
+=−+9)
30- a
8 x 0 30 a
0830 a
08
30 4a - 5a
0 4
152
aa
8
5
=
=+
=+
=+
=+−10)
ùTÚdLp
ùTÚdLp ùNnÙm ùTôÝÕ ØR≠p GpXôϱÂÓLû[Ùm, ©u× ÏQLeLû[Ùm ARu©\Ï GÝjÕLû[Ùm ùTÚdLÜm.
ERôWQm 1
ùTÚdÏL (2x-5) x (x-1)
(2x-5) (x-1)
= 2x (x-1) - 5(x-1)
= 2x2 - 2x -5x +5
= 2x2 - 7x + 5
ERôWQm 2
ùTÚdÏL (4x2 + 3x -12) by (2x +3)
(4x2 + 3x -12) (2x +3)
= 2x(4x2 + 3x -12) + 3 (4x2 + 3x -12)
= 8x3 +6x2 - 24x + 12x2 + 9x - 36
= 8x3 +6x2 + 12x2 - 24x + 9x - 36
= 8x3 +18x2 - 15x -36
YÏjRp
YÏjRp GuTÕ ùTÚdL≠u G§o Uû\ùNnûLVôÏm.
ERôWQm 1
YÏjRp (x2+ 11x + 30) by (x + 6)
(x2+ 11x + 30) ÷ (x + 6)
x2+ 11x + 30 ÷ x + 6 = x + 5
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.6.18
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§\]ônÜ T«t£ (Assignment)
áhPp
1 Add 7y, 8y, 5y , 3y
2 Add 5x, 6x, 7y - 9y, 10x
3 Add 9a2, -7m, 5, -14a2, 15m, -6
4 Add
L¯jRp
1 Subtract 7x from 9x
2 Subtract 8a from 3a
3 (-5 -3b) - (3a + 5b)
4 Subtract (5m - 6n) from (3m + 5n)
ùTÚdLp
1 Multiply 6a x (- 2ab)
2 Multiply 3x (4x - 2y + 5)
3 Multiply (3x + 2) (3x - 2)
YÏjRp
1 525x ÷
2 15a60ab ÷
3 77y14x ÷−
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.6.18
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EúXôLeL°u CVt©Vp Utßm CVk§W®Vp RuûULs T«t£ 1.7.19
EúXôLm: (Metal)
EúXôLm GuTÕ JÚ RôÕlùTôÚs.CûYGpXô ®RUô] ùTô±«Vp úYûXLÞdÏmTVuTÓjRlTÓ¡\Õ. ARôYÕ CVk§WeLs,TôXeLs, BLôV®Uô]m úTôu\Yt±pTVuTÓjRlTÓ¡\Õ. BûLVôp SômEúXôLj§u A¥lTûP A±ûY ùTt±ÚdLúYiÓm.
ùYlTm EVoRp, CÝ®ûN, CßdÏ®ûNUtßm úUôRXôp HtTÓm ®ûN úTôu\LôW¦LÞdÏ HtT Y¥YûUdLlThP TXYûLVô] TôLeLû[ JÚ ùU£²vhùNnYRtÏ Øu EúXôLeL°u CVt©VpUtßm CVk§Wj RuûUL°uØd¡VjÕYjûR ׬kÕ ùLôiPYWôLCÚjRp ªL Ød¡V úRûYVôÏm.
EúXôLj§u RuûULû[ A±kÕ CÚjRpúYûXûV ùYt±LWUôL ùNnÕ Ø¥dL ERÜm.N¬Vô] êXlùTôÚs/EúXôLm TVuTÓj§TôLeLs ùNnVlTPô®hPôp, AlTôLeLsETúVôLj§p CÚdÏm ùTôÝÕEûPYRtúLô ApXÕ úRôp®«pØ¥YûPYRtúLô Yônl× HtTÓm.
EúXôLj§u ÁÕ JúW A[®p TÞùLôÓdÏmúTôÕ TpúYß EúXôLeL°pHtTÓm ®û[ÜLû[ (TPm 1) LôhÓ¡\Õ.EÚUôt\j§u ®û[ÜLÞdLô]®j§VôNj§û] ϱjÕd ùLôs[Üm.
– LhPûUl×
– LPjÕm RuûU
– LôkRj RuûU
– EÚÏm RuûU
¨\m (Colour)
JqùYôÚ EúXôLj§tÏm CVtûL«úXúVR²jR² ¨\m EiÓ. ERôWQm ,ùNm×®j§VôNUô] £Ll× ̈ \j§p CÚdÏm, ªÚÕG@Ï FRô/LÚl× ¨\j§p CÚdÏm.
GûP (Weight)
JÚ Ï±l©hP L] A[Üs[ EúXôLeL°uGûP JtßdÏ Juß UôßTÓm.AÛª²Vj§u GûP Ïû\YôL CÚdÏm(APôój§ Gi 2.7) Utßm LôÃVj§u GûPA§LUôL CÚdÏm (APôój§ Gi 11.34)
LhPûUl× (Structure) (TPm 2 & 3)
JÚ EúXôLj§u ÏßdÏ ùYhÓ úRôt\jûRûUdúWôvúLôl êXm EúXôLeL°uAûUl©u ®j§VôNjûR A±VXôm.ùTôÕYôL EúXôLeL°u Eh×\ AûUl×ùYqúY\ôL CÚdÏm. úR²Úm× UtßmAÛª²Vj§u AûUl× Sôôó úTôußCÚdÏm Utßm Yôôól©Úm× UtßmùYiLXm ¡WôàXôó AûUl× ùLôiPRôLCÚdÏm.
EúXôLj§u CVt©Vp RuûULs (Physi-cal properties of metals)
– ¨\m
– GûP/APôój§ Gi
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LPjÕm RuûU (Conductivity) (TPm 4 & 5)
ùYlTdLPjRp Utßm ªuLPjRp RuûUJÚ RϧVô] ùTôÚ°u ùYlTjûRÙm,ªuNôWjûRÙm LPjÕm §\]ôÏm.LPjÕmRuûU JußdùLôuß UôßTÓm.ùNm×m AÛª²VØm JÚ SpX ùYlTmUtßm ªu LPj§VôÏm.
LôkRj RuûU (Magnetic property)
JÚ EúXôLm LôkRj§]ôp LYWlThPôpAkR EúXôLm LôkRjRuûU EûPVÕ GußùNôp¡ú\ôm.
£X YûL vùP«uùXv v¼pLû[j R®W,ùTÚmTôÛm GpXô CÚm× NjÕ Es[EúXôLeLÞm LôkRjRôp LYWlTÓm UtßmGpXô ®RUô] CÚm× NjÕ CpXôREúXôLeLs Utßm ARàûPV AXônB¡VYûY LôkRm LYWôÕ.
EÚÏm RuûU (Fusibility) (TPm 6)
EúXôLj§u ÁÕ ùYlTjûR ùNÛj§]ôp,§iU ¨ûX«p CÚkÕ ¿ôóU ¨ûXûVAûPÙm RuûU EÚÏm RuûU G]lTÓm.TX EúXôLeL°u EÚYj§p UôßRpHtTÓm. ARôYÕ ùYqúYß ùYlT¨ûX«pEúXôLeLs §iU ¨ûX«p CÚkÕ ¿ôóU¨ûXûV AûP¡u\Õ. Ïû\kR ùYlT¨ûX«p LôÃVm EÚÏm. AúR NUVm CÚm×A§L ùYlT ¨ûX«pRôu EÚÏm.
ùYsÇVj§u EÚÏ ¨ûX 232°C.
PevPu EúXôLj§u EÚÏ ¨ûX 3370°C.
CVk§W®Vp RuûULs (Mechanicalproperties)
– Lm©VôL ¿Þm RuûU (Ductility)
– RLPôL ¿Þm RuûU (Malleability)
– L¥]j RuûU (Hardness)
– ùSôßeÏm RuûU (Brittleness)
– §iûUj RuûU (Toughness)
– CÝ®ûNûV RôeÏm RuûU (Tenacity)
– Áh£j RuûU (Elasticity)
Lm©VôL ¿Þm RuûU (Ductility) (TPm 7)
Jo EúXôLjûR Lm©VôLj RVô¬dÏmùTôÝÕ, AÕ GkR ®R ®¬NÛdÏmEhTPôUp Lm©VôL ¿iPôp ARtÏLm©VôL ¿Þm RuûU Guß ùTVo. Lm©VôL¿Þm RuûUûVl ùTôßjÕ Ko EúXôLmLm©VôL Uôßm. CkRj RuûU EûPVEúXôLm EߧVô]RôLÜm Utßm ©[ôv¥d RuûUÙPàm CÚdL úYiÓm. ùNm×Utßm AÛª²Vm B¡VûY CjRuûUdÏ£\kR ERôWQUôÏm.
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.7.19
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Áh£j RuûU (Elasticity)
EúXôLeLs ÁÕ JÚ Ï±l©hP A[Ü YûWYõûN ùNVtTÓmùTôÝÕ AlùTôÚ[ô]ÕEÚY UôßRp AûPkÕ, ©u Aq®ûN®ÓThPÜPu ÁiÓm Ru TûZV ̈ ûXûVAûPÙm RuûUdÏ Áh£j RuûU GußùTVo. ùYlT TR²Ó ùNnVlThP v©ôõeJÚ SpX ERôWQm BÏm.
RLPôL ¿Þm RuûU (Malleability) (TPm 8 &9)EúXôLeL°u ÁÕ Ñj§VXôp A¥jRpApXÕ úWô≠e ùNnÕ GpXô §ûNL°Ûm®ôõYûPkÕ AR]ôp ®¬N≠u± RLPôLUôßm RuûU RLPôL ¿Þm RuûU G]lTÓm.LôÃVm RLPôL ¿Þm RuûUdÏ £\kR EúXôLERôWQUôÏm.
L¥]j RuûU (Hardness) (TPm10)úRnUô]jûR RôeÏYûRÙm EWÑmúTôÕúRnYûPYûRÙm ¸\pLs HtTÓYûRÙmG§ôódÏm RuûU L¥]jRuûU G]lTÓm.AWjRôp ϱÂÓ ùNnÕ L¥]j RuûUûVúNô§jÕ A±VXôm.
ùSôßeÏm RuûU (Brittleness) (TPm 11)
EúXôLeLs EûPÙYRtÏ Øu]ôp ¨WkRWEÚY Uôt\j§tÏ B[ôLôUp EûPÙmRuûU BÏm. Yôôól©Úm× JÚ £\kRERôWQUôÏm. CÕ A§oÜ (A) úUôR≠]ôpYû[VôUp ùSôßeÏm RuûU EûPVRôÏm.
§iûUj RuûU (Toughness) (TPm 12)
EúXôLeLs úUôRXôúXô A§ôóf£VôúXôEûPVôUp AûR G§ôóójÕ ̈ tÏm RuûUúV§iûUj RuûU G]lTÓm. úR²Úm× CRtÏJÚ £\kR ERôWQUôÏm.
CÝ®ûNûV RôeÏm RuûU (Tenacity)
EúXôLeLs ÁÕ CÝ®ûNLsùNVpTÓmùTôÝÕ EûPVôUp G§ôójÕCÚdÏm RuûU CÝ®ûNûV RôeÏm RuûUG]lTÓm. ªÚÕ G@Ï, úR²Úm×, UtßmùNm× B¡V EúXôLeLs ùP]ô£h¥dÏ£\kR ERôWQeLs BÏm.
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.7.19
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CÚm× Utßm Yôol× CÚm©tLô] A±ØLm T«t£ 1.7.20
CÚm×fNjÕs[ EúXôLeLs (Ferrous Met-als)A§L A[®p CÚm×NjÕ ùLôiPEúXôLjûR CÚm×fNjÕs[ EúXôLm G]AûZd¡ú\ôm. TpúYß úRûYLÞdÏTpúYß RuûUÙûPV CÚm×fNjÕs[EúXôLeLs TVuTÓjRlTÓ¡u\].
CÚm×, Yôol× CÚm×, úR²Úm×, UtßmG@Ï B¡VYt±u A±ØLm
ùTôÕYô] TVuTôh¥p Es[ CÚm×fNjÕs[ EúXôLeL[ôY]:
– L² CÚm× (Pig Iron)
– Yôol× CÚm× (Cast Iron)
– úR²Úm× (Wrought Iron)
– G@Ï Utßm LXl× G@Ï (Steels and Alloysteels)
CÚm× Utßm G@ÏLs TX ùNnØû\Lû[TVuTÓj§ RVôo ùNnVlTÓ¡\Õ.
L² CÚm× (Pig Iron) RVô¬dÏm Øû\
úY§Vp RuûU EûPV CÚm×fNjûRÏû\jÕ L² CÚm× ¡ûPdLl ùTß¡\Õ.CqYôß CÚm×fNjûR Ïû\jÕ L² CÚm×RVô¬dÏm Øû\ûV vùUp¥e (SMELTING)Guß A±¡ú\ôm.
L² CÚmûT RVô¬dLj úRûYVô]êXlùTôÚhLs;
– CÚm× RôÕ (Iron ore)
– Tô§ ÑhP ̈ XdL¬ (Coke)
– C[d¡ (Flux)
CÚm× RôÕ (Iron ore)
TVuTÓjRlTÓm Ød¡V CÚm× RôÕdLs.
– úUd]ûPh (magnetite)
– úaUûPh (hematite)
– ≠úUôû]h (limonite)
– LôoTú]h (carbonate)
úUtá±V RôÕdL°p CÚm× TX®¡ReL°pLXkÕ Es[Õ úUÛm CûYLs CVtûLVôL¡ûPd¡u\].
Tô§ ÑhP ¨XdL¬ (Coke)
Tô§ ÑhP ̈ XdL¬ úRûYVô] A[®tÏ CÕùYlTjûR ùLôÓdL G¬lùTôÚ[ôLTVuTÓjRlTÓ¡\Õ. úLôd¡p, LôoTuúUô]ôdûNPôL Es[ LôoTu RôÕÜPuúNokÕ CÚmTôL Uôt±d ùLôÓd¡\Õ.
C[d¡ (Flux)
CÕ JÚ RôÕl ùTôÚs FÕ EûX«u (Blastfurnace) A¥lTôLj§p ùNÛjRlTÓ¡\Õ. CRuêXm RôÕdLs EÚÏ ̈ ûXûV AûP¡u\Õ.CÕ EúXôLUt\ TϧÙPu CûQkÕ EÚ¡VLNPôL EÚYô¡u\Õ.
FÕ EûX«p ùTÚmTôÛm ÑiQôm×LtLû[úV C[d¡VôL TVuTÓjÕ¡u\]o.
L² CÚm©u RuûULs Utßm TVuLs(Properties and use of Pig-iron)L² CÚmûT Ñj§L¬jÕ Utßm ÁiÓmEÚd¡ TX®RUô] CÚm× Utßm G@ÏLsRVôo ùNnVlThÓ TVuTÓjRlTÓ¡\Õ.
Yôol× CÚm× Cast Iron (RVô¬dÏm Øû\)
L² CÚm×, FÕ EûX«p CÚkÕ LNPôL,WôùUh¥¬VXôL ÏlúTôXô®p ùNÛjÕYRtLôL AÕ ÁiÓm Ñj§L¬dLlTÓ¡\Õ.CqYôß Ñj§L¬dLlThPÕ ÏlúTôXôEûX«u CPlTÓ¡\Õ CÕ JÚ £±V FÕEûXVôÏm.
ùTôÕYôL ÏlúTôXô EûX FÕ EûX úTôXùRôPokÕ úYûX ùNnVôÕ. úRûYlTÓmùTôÝÕ UhÓm AûR TVuTÓj§dùLôs[Xôm.
Yôol× CÚm× (YûLLs) (Cast Iron)CÚm×, LôoTu Utßm £≠dLôu LXûYRôuYôol× CÚmTôÏm. C§p 2 ØRp 4 ®ÝdLôÓLôoTu Es[Õ.
Yôol× CÚm©u YûLLs
Yôol× CÚm©u YûLLs ¸úZùLôÓdLlThÓs[];
– NômTp ¨\ Yôol× CÚm× (Grey cast iron)
– ùYsû[¨\ Yôol× CÚm× (White cast iron)
– úU≠V©p Yôol× CÚm×(Malleable cast iron)
– Öi EÚiûP Yôol× CÚm× (Nodular castiron)
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NômTp ¨\ Yôol× CÚm× (Grey cast iron)
CVk§Wj§u TôLeLû[ RVô¬dL Utßm ªLG°§p ùU£²e ùNnV NômTp ¨\ Yôol×CÚm× A§L A[®p TVuTÓjRlTÓ¡\Õ.
CVk§Wj§u A¥lTôLm, úP©sLs,TdLeLs B¡VûYLs Yôol× CÚmTôpùNnVlTÓ¡\Õ. Hù]²p Sôs TPEûZdÏm Utßm A[ÅPôL ¨ûXVôLCÚdÏm.
C§p ¡WôlûTh LXkÕ CÚlTRôp, úT¬eUtßm SLÚm TWl× Yôol× CÚmTôpùNnVlTÓ¡\Õ.
CÚmûTdLôh¥Ûm CRu EÚÏ ̈ ûX Ïû\Ü.£\kR §WYUôLÜm, £dLXô] Yôol×Lû[ùNnVÜm NômTp ¨\ Yôol× CÚm×TVuTÓ¡\Õ.
CVk§W LÚ®Lû[ ùNnYRtÏ NômTp ¨\Yôol× CÚm× A§L A[®pTVuTÓjRlTÓ¡\Õ Hù]u\ôp A§of£ûVÏû\d¡u\Õ, Utßm LÚ® ¡Ó ¡Ó G]BÓYûR RÓd¡u\Õ.
NômTp ̈ \ Yôol× CÚm× LXl× EúXôLUôLCpXôUp CÚkRôp CÝ®ûN ªLÜmÏû\YôL Es[Rôp G°§p EûPkÕ ®Óm.CdLôWQjRôp A§L ®ûN ApXÕ §¼ùW]HtTÓm TÞ YWdá¥V CVk§W TôLeLsCR]ôp RVôo ùNnVlTÓYÕ CpûX.
¨dLp, ÏúWôªVm, Y]¥Vm ApXÕ ùNm×B¡VûY TX úSWeL°p NômTp ̈ \ Yôol×CÚm×Pu LXkÕ L¥]jRuûUEiPôdLlTÓ¡\Õ.
NômTp ¨\ Yôol× CÚmûT Tt\ ûYdLCVÛm. B]ôp A¥lTûP EúXôLjûRØR≠p ùYlTlTÓjRúYiÓm.
ùYsû[ ̈ \ Yôol× CÚm× (White cast iron)
CÕ ªLÜm L¥]Uô] EúXôLm, ùU£uùNnYÕ L¥]m. AR]ôp úRnUô]jûRG§odÏm CVk§Wj§u TôLeLû[ RVôoùNnV TVuTÓjRlTÓ¡\Õ.
£≠dLôû] Ïû\jÕ Utßm úYLUôL Ï°o®jRp êXm ùYsû[ Yôol× CÚm×RVô¬dLlTÓ¡\Õ. CqYôß Ï°o®lTRôpCÕ Ï°okR Yôol× CÚm× GußmAûZdLlTÓ¡\Õ..
ùYsû[ Yôol× CÚmûT Tt\ ûYdLCVXôÕ.
úU≠V©p Yôol× CÚm× (Maileable castiron)
úU≠V©p Yôol× CÚmûT NômTp ¨\Yôol× CÚm×Pu Jl©Óm ùTôÝÕPd¥≠¥, CÝ®ûN, §iûUj RuûUB¡VûY áÓRXôL CÚd¡u\Õ.
ùYsû[ Yôol× CÚmûT ¿iP úSWm ùYlTTR²ÓRp ARôYÕ 30 U¦ úSWj§tÏ ùNnÕúU≠V©p Yôol× CÚm× RVô¬dLlTÓ¡\Õ.
Öi EÚiûP Yôol× CÚm× (Nodular castiron)
CÕ úU≠V©p Yôol× CÚm× úTôXúYCÚdÏm. B]ôp GkR ®RUô]ùYlTTR²ÓRÛm úRûY CpûX. ÖiEÚiûP Yôol× CÚm×, ùSôÓXo CÚm×PdûPp CÚm× vùToWônPp ¡WôlûTh(Spheroidal Graphite Iron) CÚm× GußmA±VlTÓ¡\Õ.
CÕ SpX ùU£²e RuûU, Yôol× ùNnÙmRuûU, úRnUô]jûR G§odÏm RuûU,Ïû\kR EÚÏ ¨ûX Utßm L¥]jRuûUEûPVÕ.
úU≠V©p Utßm Öi EÚiûP YôolûTTVuTÓj§ CVk§Wj§u TôLeLs RVôoùNnVlTÓ¡\Õ. A§L A[Ü CÝ®ûN UtßmSÓjRWUô] CmTôdh úXôÓ RôeLdá¥VTôLeLs RVôo ùNnVlTÓ¡\Õ. CÕ Ïû\kRùNX®p Yôol× ùNnVlTÓ¡\Õ. CÕ CÚm×Yôol©tÏ Uôt\ôÏm.
úR²Úm× (Wrought Iron) (RVô¬dÏm Øû\)(TPm 1)
CÚm©p Es[ L¯Ül ùTôÚhLû[ ¿d¡RVô¬dLlTÓm ÑjRUô] CÚm× úR²Úm×G]lTÓm. úR²ÚmûT TÏjRôp A§p 99.9®ÝdLôÓ CÚmTôÏm (TPm 1). úR²ÚmûTùYlTlTÓj§]ôp EÚLôÕ. B]ôp C[Ïm.Ck¨ûX«p CûR GkR Y¥Yj§Ûm úTôo_õÓùNnVØ¥Ùm.
SÅ] Øû\ûV TVuTÓj§ úR²ÚmûT ùT¬VA[®p EtTj§ ùNnVØ¥Ùm Øû\L[ôY]
– ×h≠e ùNnØû\ (puddling process)
– AvPôu (A ) ûTVov ùNnØû\(aston or Byers process)
G@Ï (Steel)
CÕ ÑjRUô] CÚm×, LôoTu A§LUôLCÚdÏm. LôoTu áÓRXôL CÚlTRôp CÕ
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.7.20
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EߧVô]úRô CpûX. NôRôWQ Øû\«pCûR aôoPú]ô ApXÕ ùPmTúWôùNnVØ¥VôÕ. Sh, úTôph, ¬®h, RLÓ,JVo, T AVou Utßm Be¡p AVouØR≠VûYLs CR]ôp RVôoùNnVlTÓ¡\Õ.
B SÓjRW LôoTu G@Ï: 0.25 ØRp 0.5®ÝdLôÓ LôoTu Es[Õ. LôoTuA§LUôL CÚlTRôp ªÚÕ G@ûLLôh¥Ûm L¥]Uô]Õ Utßm§iûUVô]Õ Utßm ùP]ô£h¥ A§Lm.CûR L¥]jRuûU ApXÕ ùPmToùNnVXôm. úTôo_õe Utßm úWô≠e êXmTX®RUô] ùTôÚhLs RVôoùNnVlTÓ¡\Õ. A§L CÝ®ûN ùLôiP¥ël×Ls, JVoLs, ®YNôV LÚ®Ls,CûQl× WôÓLs, úLm`ôlh, vúT]oUtßm Ll©Ls úTôu\Ytû\ ùNnVTVuTÓjRlTÓ¡\Õ.
C A§LUô] A[Ü LôoTu Es[ G@Ï:C§p LôoTu A[Ü 0.5 ØRp 1.5 ®ÝdLôÓCÚdÏm. CÕ ªLÜm L¥]Uô]Õ UtßmÏû\kR úRnUô]m ùLôiPÕ. ùYlTTR²ÓRp êXm CûP L¥]UôdLXôm.CûR YôolúTô ApXÕ úWôpúXô ùNnVØ¥VôÕ. CÕ ªLÜm L¥]Uô]Õ,§iûUVô]Õ. CÕ ̈ ûXVô] LôkR Nd§ùLôiPÕ. áoûUVô] LÚ®Ls, v©¬e,LhX¬v, Tm×Ls, AWm, úLôpÓ £Np,©WvûP ØR≠V] CkR G@¡]ôp RVôoùNnVlTÓ¡\Õ.
2 LXl× G@Ï (Alloy Steel)≠ú]ô≠Vm, UôeLÉv, PevPu úTôu\EúXôLeLû[ G@ÏPu LXkÕ RVôoùNnVlTÓm EúXôLm LXl× G@Ï G]lTÓmCkR LXl× EúXôLj§u RuûULsêXlùTôÚhLû[ ùTôÚjRÕ.
LXl× G@¡u YûLLs
Ød¡VUô] CWiÓ YûL LXl× G@ÏLs:
A Ïû\kR LXl× G@Ï (Low alloy steel)
B A§L LXl× G@Ï (High alloy steel)
A Ïû\kR LXl× G@Ï: LôoTu R®W Ut\EúXôLeLs Ïû\kR A[®p CÚdÏm.C§p CÝ®ûN §\u A§LUôL Es[Õ.CûR ùYp¥e ùNnV CVÛm. CûRL¥]lTÓjRÜm Utßm ùPmTÚm ùNnVØ¥Ùm. ®Uô]j§u TôLeLs Utßm úLm`ôlh (cam shaft) úTôu\Ytû\ RVôo ùNnVTVuTÓjRlTÓ¡\Õ.
L¥]UôLÜm Utßm §iûUVôLÜm CÚdÏm.C§p 0.15 ØRp 1.5 ®ÝdLôÓ LôoTu LXkÕEs[Õ. C§p NpTo, TôvTWv úTôu\ Ut\úRûYVt\ ùTôÚhLÞm LXkÕ Es[Õ.B]ôp CûYLû[ R²VôL ©¬dL CVXôÕ.JÚ Ï±l©hP ùYlT ̈ ûX«p ùYlTlTÓj§AÕ GiùQn ApXÕ Ri½WôpÏ°o®dLlThÓ aôoPu Utßm ùPmToùNnVlTÓ¡u\Õ.
TXYûLVô] G@ÏLû[ RVô¬dL ̧ rLiPØû\Ls TVuTÓjRlTÓ¡u\].
1 £ùUiúPNu ùNnØû\(Cementation process)2 ÏÚ£×p ùNnØû\ (Crucible process)3 ùT£Uo ùNnØû\ (Bassemer process)4 KlTu ùaoj ùNnØû\ (Open hearth process)5 GXdhúWô ùRoúUô ùNnØû\ (Electro thermo
process)6 ûa ©¬dÏYu£ ùNnØû\ (High frequency
process)11 .13 G@¡u Ød¡VUô] YûLLs:
Ød¡VUô] CWiÓ YûL G@ÏLs
1 NôRôWQ G@Ï (Plain steel)2 AXôn G@Ï (Alloy steel)1 NôRôWQ G@Ï (Plain steel). C§p LôoTàm
CÚm×m LXkÕ CÚd¡u\Õ. LôoTu®ÝdLôÓdÏ HtT NôRôWQ G@ϸrLiPYôß ©¬dLlThÓs[Õ.
A Ïû\kR LôoTu G@Ï (Low carbon steel)B SÓjRW LôoTu G@Ï (Medium carbon steel)C A§LUô] A[Ü LôoTu Es[ G@Ï
(High carbon steel)A Ïû\kR LôoTu G@Ï: CÕ ªÚÕ G@Ï
Gußm AûZdLlTÓ¡\Õ. 0.15 ØRp 0.25®ÝdLôÓ LôoTu Es[Õ. CqYôßÏû\kR A[Ü LôoTu Es[RôpúRûYVô] A[®tÏ ªÚÕYôLEs[Rôp §¬×ûY (strain) RôeÏm úTôo_õeUtßm úWô≠e êXm TX Y¥YeL°pCûR AûUdL CVÛm. CÕ L¥]Uô]úRô,
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.7.20
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B A§L LXl× G@Ï: LôoTu R®W Ut\EúXôLeLs úXô AXônv¼ûXdLôh¥Ûm A§L ®ÝdLôÓ LXkÕCÚdÏm. CÕ ̧ rLiPYôß YûLlTÓjRlThÓs[Õ.
a ûa vÀÓ v¼p (High Speed Steel):CÕ ûa PevPu AXôn v¼p GußmAûZdLlTÓm. Hù]u\ôp C§p A§LA[Ü PevPu LXkÕ Es[Õ. PevPuA[ûYl ùTôÚjÕ êuß YûLVôL©¬dLlThÓs[Õ.
1 PevPu 22%, ÏúWôªVm4%, Y]¥Vm 1%
2 PevPu 18%, ÏúWôªVm 4%, Y]¥Vm 1%
3 PevPu 14%, ÏúWôªVm 4%, Y]¥Vm 1%
C§p ùYhÓ LÚ®Ls ùNnVlTÓ¡\Õ.Hù]u\ôp CÕ ªLÜm L¥]Uô]Õ, B]ôpÏû\kR ¡¬h¥Lp ùYlTj§p ªÚÕ RuûUAûPÙm. ùYhÓm LÚ® ùNVpTÓm ùTôÝÕùYlTm A§L¬jRôp, ùYhÓm LÚ®TV]t\Rô¡®Óm. úUÛm úYûX ùNnÙmRϧûV CZkÕ ®Ó¡\Õ. B]ôp A§L®ÝdLôÓ PevPu CÚlTRôp, A§LùYlTj§Ûm CÕ úYûX ùNnÙm.ùYhÓdLÚ®, ¥¬pv, LhPo, ÃUo, BdNô©ú[Ó ØR≠V]Ytû\ ùNnV TVuTÓ¡\Õ.
b ¨dLp v¼p (Nickel Steel):C§p LôoTu 3 ®ÝdLôÓ, ¨dLp 0.25 ØRp0.35 ®ÝdLôÓ Es[Õ. ¨dLp LXkÕCÚlTRôp CÝ®ûN,Áh£«Vp GpûXUtßm L¥]jRuûU A§L¬d¡u\Õ. CÕÕÚl©¥dLôÕ. 0.35 ®ÝdLôÓ ¨dLp LXkÕEs[Rôp, ùYhÓm §\u NôRôWQ LôoTuv¼ûXd Lôh¥Ûm 6 UPeÏ A§Lm. ¬®h,ûTl, Bd£p, ̀ ôlh úTÚkÕL°u TôLeLsUtßm ®Uô]eLs B¡VûYLû[ RVôoùNnV TVuTÓjRlTÓ¡\Õ. 5 ®ÝdLôÓúLôTôph, 30 ØRp 35 ®ÝdLôÓ ̈ dLÛPuLXdÏm ùTôÝÕ CuYôo v¼p -BLUôß¡u\Õ. Ød¡VUôL ®ûX EVokRLÚ®Ls RVô¬dL TVuTÓjRlTÓ¡\Õ.
c Y]¥Vm v¼p (Vanadium Steel):C§p 1.5 ®ÝdLôÓ LôoTu, 12.5 ®ÝdLôÓPevPu, ÏúWôªVm 4.5 ®ÝdLôÓ, Y]¥Vm5 ®ÝdLôÓ Utßm úLôTôph 5 ®ÝdLôÓLXkÕ CÚdÏm. CRu Áh£«Vp GpûX,CÝ®ûN Utßm Pd¥≠h¥ A§Lm CÚdÏm.`ôol A§oûY RôeÏm YpXûU Es[Õ.Ød¡VUôL LÚ®Ls RVô¬dL TVuTÓjRlTÓ¡\Õ.
d UôeLÉv v¼p (Manganese Steel):CÕÜm vùTNp ûa AXôn v¼p GußAûZdLlTÓ¡\Õ. C§p 1.6 ØRp 1.9®ÝdLôÓ UôeLÉÑm Utßm 0.4 ØRp 0.5®ÝdLôÓ LôoTàm LXkÕ Es[Õ. CÕL¥]Uô]Õ Utßm Ïû\kR úRnUô]mEûPVÕ. LôkRjRôp Tô§dLôÕ CÕ¡ûWiPo Utßm W«p Tô«ihL°pTVuTÓjRlTÓ¡\Õ.
e vùP«uùXv v¼p (Stainless Steel):CÕ CÚmúTôÓ 0.2 ØRp 90.6 ®ÝdLôÓLôoTu, 12 ØRp 18 ®ÝdLôÓ ÏúWôªVm, 8®ÝdLôÓ ¨dLp, 2 ®ÝdLôÓ Uô≠l¥]m(molybdenum) LXkÕ Es[Õ. Lj§Ls, Lj§¬dúLôpLs, Tôj§WeLs, ®Uô] TôLeLs,JVo, ûTl×Ls Utßm ¡VoLs úTôu\Ytû\RVô¬dL TVu TÓjRlTÓ¡\Õ.
vùP«uùXv v¼≠u RuûULs(Properties of stainless steel):1 A§L A¬Uô] G§ol×jRuûU
2 A§L LÓeÏ°o §iûUjRuûU
3 A§L L¥]UôdÏm RuûU
4 A§L ùYlTjRôeÏ §\u
5 A§L RLPôL ¿Þm RuûU
6 A§L RôeÏ¡\u Utßm L¥]j RuûU
7 SuÏ LYÚm úRôt\m
8 Ïû\kR TWôU¬l×
f £≠Lôu v¼p (Silicon Steel):C§p 15 ®ÝdLôÓ £≠dLôu Es[Õ,£≠dLôu A[ûYl ùTôßjÕ TpúYß YûLCÚm×f NjÕs[ EúXôLj§p TVuTÓjRlTÓ¡\Õ. 0.5 ®ÝdLôÓ ØRp 1 ®ÝdLôÓ£≠dLôu 0.7 ®ÝdLôÓ ØRp 0.95 ®ÝdLôÓUôeLÉÑ LXkÕ LhÓUô] úYûXLÞdÏTVuTÓjRlTÓ¡\Õ. 2.5 ØRp 4 ®ÝdLôÓ£≠dLôu LXûY êXm ªuNôWúUôhPôoù_]úWhPo, ¥WôuvTôoUÚdLô] úXªú]Nu B¡VûYLsEtTj§ ùNnVlTÓ¡u\]. WNôV]ùRô¯tNôûX«p 14 ®ÝdLôÓ £≠dLôuLXûY TVuTÓjRlTÓ¡\Õ.
g úLôTôph v¼p (Cobalt Steel):ûa LôoTu v¼≠p 5 ØRp 35 ®ÝdLôÓúLôTôph LXkÕ Es[Õ CRu §iûUjRuûU Utßm ùP]ô£h¥ (Toughness andtenacity) A§Lm. CRtÏ LôkR Nd§ EiÓ,AR]ôp ¨ûXVô] LôkRm EÚYôdÏYRtÏTVuTÓjRlTÓ¡\Õ.
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.7.20
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CÚm×fNjÕs[ Utßm CÚm×fNj§pXôR EúXôL YûLLs T«t£ 1.7.21
CÚm×fNjÕs[ Utßm CÚm×fNj§pXôR LXl× EúXôLeLs
CÚm×fNjÕs[ LXl× EúXôLm UtßmARàPu LXdÏm EúXôLeLs (Alloyingmetals and ferrous alloys)
CWiÓ (A ) CWiÓdÏ úUtThPEúXôLeLû[ EÚd¡ EÚYôd¡]ôp LXl×EúXôLm ¡ûPdÏm.
CÚm×fNjÕs[ EúXôLeLs Utßm LXl×EúXôLeLÞdÏ ªL Ød¡VUô] EúXôLmCÚm× BÏm. EÚd¡ CûQdÏmEúXôLj§u TeÏ Utßm YûL B¡VYtû\lùTôÚjÕ LXl× G@¡u RuûU UôßTÓm.
AXôn v¼p RVôôõdL ùTôÕYôLTVuTÓjRlTÓm EúXôLeLs
¨dLp (Ni) (Nickel)
CÚ JÚ L¥]Uô] EúXôLm. TX YûLVô]A¬Uô]eLû[ G§ôódÏm RuûUÙûPVÕ.
CÚ ùRô¯tNôûX«p EtTj§«p, ARôYÕ¨dLp, LôhªVm úThPôõLs, TônXôó ¥ël,CuPôó]p LmTvPu CVk§Wj§uYôpÜLs, CVk§Wj§u vTôôód ©[dÏLsØR≠V] RVô¬dL TVuTÓ¡\Õ. ¨dL≠uEÚÏ ¨ûX 1450°C. ¨dLÛdÏ LôkR RuûUEiPôdLXôm. ¨ûXVô] LôkR Nd§EiPôdL ©Wj§úVLUôL ̈ dLp v¼p AXônTVuTÓ¡\Õ. ªu ØXôm éÑYRtÏ ¨dLpTVuTÓjRlTÓ¡\Õ. CuYôôó v¼≠p 36®ÝdLôÓ ¨dLp Es[Õ. CÕ L¥]Uô]ÕUtßm A¬Uô]j§tÏ G§Wô]Õ. CuYôôóv¼p êXm ®ûX EVôókR LÚ®Ls RVôôóùNnVlTÓ¡\Õ, Hù]u\ôp CuYôôóv¼ÛdÏ ¿[ ùTÚdÏ Gi ªLÜm Ïû\Ü.
¨dLp þv¼p LXl× EúXôLj§p, ¨dLp 2ØRp 50®ÝdLôÓ LXkÕ Es[Õ.
ÏúWôªVm (Cr) (Chromium)
ÏúWôªVjûR G@ÏPu úNôójRôp AÕÕÚ©¥lTûR RÓdÏm, L¥]jRuûU Utßmv¼≠u Eߧ A§LôõdÏm. 30 ®ÝdLôÓÏúWôªVm Es[ ÏúWôªVm v¼p¡ûPd¡u\Õ.
ÏúWôªVjÕPu, ¨dLp, PevPu UtßmUô≠l¥]m LXdLlTÓYRu êXmRô²Ve¡L°u TôLeLs Utßm Lh¥eåpLs RVôôõdLlTÓ¡\Õ.
TôLeLû[ ªu ØXôm éÑYRtÏ, ÏúWôªVmTVuTÓ¡\Õ. £≠iP¬u ûXu]ôõuEhTϧ«p ÏúWômþ©ú[h ùNnVlTÓ¡\Õ.CR]ôp úRnUô]jûR G§ôódÏm Bt\pA§Lôõd¡\Õ. vGP«uùXv v¼≠p 13®ÝdLôÓ ÏúWôªVm Es[Õ. ÏúWôªVm¨dLp v¼p, úTôõe ùNnV TVuTÓ¡\Õ.ûLdLÚ®Ls ARôYÕ vTô]ôóLs UtßmôõgNv (wrenches) B¡VûYLs RVô¬dLÏúWôªVmþY]¥Vm v¼p ETúVôLlTÓjRlTÓ¡\Õ.
UôeLÉÑ (Mn) (Manganese)
v¼ÛPu UôeLÉûN úNô ójRôpL¥]jRuûUÙm, EߧÙm A§Lôõd¡u\Õ.B]ôp Ï°ôóf£ ¨ûX Ïû\¡u\Õ.
LÚ®L°u ×\lTWlûT L¥]lTÓj§úRnUô]jûR Ïû\dL UôeLÉÑTVuTÓjRlTÓ¡\Õ. 14 ®ÝdLôÓ ùLôiPUôeLÉÑ v¼p, ®YNôVm NmTkRlThPLÚ®Ls ùNnV ARôYÕ EZÜ LÚ®Ls Utßm©ú[ÓLs ùNnV TVuTÓjRlTÓ¡\Õ.
£≠dLôu (Si) (Silicon)
v¼ÛPu £≠dLôû] úNôójRôp, A§LùYlTjRôp Bd£úPNu HtTÓYûR RÓdÏmNd§ v¼ÛdÏ A§Lôõd¡u\Õ. CR]ôpÁh£Vp RuûU A§LôõdÏm UtßmÕÚ©¥lTûR RÓdÏm. v©ôõe Utßm£XYûLVô] v¼pLs ÕÚ©¥dLôUp CÚdL£≠dLôu LXl× G@Ï TVuTÓjRlTÓ¡\Õ.
Yôôól× CÚm©p 2.5% ®ÝdLôÓ £≠dLôuLXkÕ Es[Õ. CÕ ¡WôlûTh EÚYôLERÜ¡\Õ. CRu LôWQUôL Yôôól× CÚm©uùU£u ùNnVlTÓm RuûU A§L¬d¡\Õ.
PevPu (W) (Tungsten)
PevP²u EÚÏ ¨ûX 3380° C CûR ªLùUp≠V Lm©VôL ùNnV Ø¥Ùm.
CdLôWQjRôp ªuNôW ®[dÏL°u©≠ùUuPôL TVuTÓ¡\Õ.
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A§L úYL ùYhÓm LÚ® RVôôó ùNnVPevPu LXl× EúXôLm TVuTÓ¡\Õ.PevPu 18 ®ÝdLôÓ, ÏúWôªVm 4®ÝdLôÓ Utßm Y]¥Vm JÚ YõÝdLôÓA[®p A§úYL v¼p AXô«p Es[Õ.
vùPpûXh Gu\ AXô«p ÏúWôªVm 30®ÝdLôÓ, PevPu 20 ®ÝdLôÓ,LôôóTu 1ØRp 4 ®ÝdLôÓ ªÏ§ úLôTôph LXkÕCÚdÏm.
Y]¥Vm (Va) (Vanadium)
CÕ v¼≠u L¥]jRuûUûVA§Lôõd¡u\Õ. ¡Vôó, LÚ®Ls ØR≠VûYY]¥Vm v¼p êXm RVôôó ùNnVlTÓ¡\Õ.v¼p LÚ®Lû[ ªL úSôój§Vô] ÕLsLhPûUl©p (fine grain) RVôôõdL Y]¥VmTVuTÓ¡\Õ.
ÏúWôm Y]¥Vm v¼≠p, ÏúWôªVm 0.5ØRp 1.5 ®ÝdLôÓ, Y]¥Vm 0.15 ØRp 0.3®ÝdLôÓ LôôóTu 0.13 ØRp 1.10 ®ÝdLôÓLXkÕ CÚdÏm.
CkR AXôn, A§LUô] CÝ®ûNûVdùLôiPÕ, Áh£«Vp GpûX, UtßmPd¥≠h¥ ùLôiPÕ. CkR AXôûVTVuTÓj§, v©ôõe ¡Vôó, ̀ ôlh Utßm ¥WôlúTôôó_õÓ TôLeLs RVôôóùNnVlTÓ¡\Õ.
Y]¥Vm ûa vÀÓ v¼≠p LôôóTu 0.70®ÝdLôÓ, Y]¥Vm 10 ®ÝdLôÓ Es[Õ.CqYôß AûUkÕ CÚkRôp AÕ EVôóókRûavÀÓ v¼p G]lTÓm.
úLôTôph (Co) (Cobalt)
úLôTôp¥u EÚÏ ¨ûX 1495°C. CÕLôkRjRuûUûV ¨ûX ¨ßj§d ùLôsÞm.ªÏkR ùYlT ¨ûX«Ûm úRnUô]jûRG§ôódÏm RuûU EûPVÕ. áôóûUVô]ùYhÓ Øû]ûV EûPV LÚ®Ls, TôpúTôõev, LôkRm úTôu\Ytû\ RVôôõdLúLôTôph TVuTÓ¡\Õ. úLôTôphûavÀhv¼p (£X NUVeL°p ãlTôó H.S.S.G]lTÓm) C§p 5 ØRp 8 ®ÝdLôÓúLôTôph CÚdÏm. 18 ®ÝdLôÓ PevPuH.S.S. I Lôh¥Ûm C§p L¥]jRuûUÙmúRnUô] G§ol×j RuûUÙm A§Lm.
úUô≠l¥]m (Mo) (Molybedenum)
CRu EÚϨûX 2620°C. ùYlTlTÓjÕmùTôÝÕ ªÚÕ RuûUdÏ G§WôLùNVpTÓ¡\Õ. úUô≠l¥]m ûavÀh
v¼≠p 6 ®ÝdLôÓ úUô≠l¥]m, 6 ®ÝdLôÓPevPu, 4 ®ÝdLôÓ ÏúWôªVm Utßm 2®ÝdLôÓ Y]¥Vm Es[Õ. CqYûL v¼pªLÜm L¥] RuûUÙm Utßm SpX ùYhÓRuûUÙm ùLôiPÕ.
LôhªVm (cd) (Cadmium)
LôhªVj§u EÚÏ ¨ûX 320°C. v¼pTôLeLÞdÏ úUtéfÑ éN TVuTÓ¡\Õ.
CÚm×fNj§pXôR LXl× EúXôLeLsUtßm ARàPu LXdÏm EúXôLeLs
CÚm× Nj§pXôR EúXôLeLs UtßmLXl× EúXôLeLs
ùNm× Utßm ARu LXl× EúXôLeLs
CÚm× NjÕ CpXôR EúXôLm Sôu ùTôóWvEúXôLm G] AûZdLlTÓ¡\Õ. ERôWQmùNm×, AÛª²Vm. ÕjR SôLm LôÃVm UtßmùYsÇVm.
ùNm× (Copper)
UôXûNh Gu\ RôÕ®p CÚkÕ ùNm×RVôôóùNnVlTÓ¡\Õ. C§p 55 ®ÝdLôÓùNm×m Utßm ûTûWhv C§p 32 ®ÝdLôÓùNm× LXkÕ CÚdÏm.
RuûULs (Properties)
ùNmùTôu ̈ \m. CRu ̈ \jûR ûYjÕ G°§pA±VXôm.
AûUlûT ©[ÜTÓj§]ôp ¡WôàXôLúRôußm. CûR úTôôó_ó ApXÕ úWôpÓùNnRôp CÕ ûTTôó BL úRôußm.
C§p PdûPp Utßm úUp≠VTp RuûUA§Lm. AR]ôp CûR RLPôLúYô ApXÕLm©VôLúYô Uôt\Xôm.
ªuNôWjûR G°§p LPjÕm ùNmûTTVuTÓj§ ªuNôW úL©s Utßm ªuNôR]LÚ®L°u TôLeLs RVôôó ùNnVlTÓ¡\Õ.CûYLs ªuNôWjûR LPjR TVuTÓjRlTÓ¡\Õ.
ùNm× JÚ SpX ùYlTd LPj§,ÕÚl©¥lTûR G§ôódÏm. CRu LôWQUôLùLô§LXu ùSÚl×ùTh¥, Ri½ûWùYlTlTÓjÕm LÚ®Ls, CWNôV]ùRô¯tNôûXLs Utßm Y¥lTôûXL°pRi½o ÏZônLs Utßm LXuLs TVuTôh¥p ETúVôLlTÓjRlTÓ¡\Õ. úUÛmNôpP¬e AV¬u RVô¬dL TVuTÓjRlTÓ¡\Õ.
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.7.21
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ùNm©u EÚÏ ¨ûX 1083o C.
úaUôõe ApXÕ úWô≠e ùNnÕ ùNm©uCÝ®ûNûV A§L¬dLXôm.
ùNm×LXl× EúXôLm (Copper Alloys)
©jRû[ (Brass)
©jRû[,ùNmûTÙm ÕjRSôLjûRÙm LXkÕùNnVlTÓm Kôó AXôn BÏm. £X YûL©jRû[Ls, £±R[Ü ùYsÇVm ApXÕLôÃVm LXkÕ ùNnVlTÓ¡\Õ. ApXô«uêXlùTôÚ°u ®ÝdLôhûP ùTôÚjÕ©jRû[«u ¨\m AûUÙm. CRu ¨\mUgNs ApXÕ CúXNô] UgNs ApXÕùYiûUVôL CÚdÏm. G°§p ùU£²eùNnVXôm, ©jRû[A¬Uô]jûR G§odÏmRuûUÙûPVÕ.
úUôhPôó Lôôõu úW¥úVhPôó úLôôó UtßmRi½ôó ÏZônLs ØR≠V] ùNnYRtÏ A§LA[®p ©jRû[ TVuTÓjRlTÓ¡\Õ. CÕúUÛm L¥]UôL úNôpPôõe ©úW£e êXmúLv Tt\ûYl× B¡VYt±tÏ TVuTÓ¡\Õ.©jRû[«u EÚÏ ̈ ûX 880 ØRp 930oC. YûWCÚdÏm.
TX®R ®¡ReL°p ©jRû[ RVôôó ùNnÕA§p TpúYß ETLWQeLs RVôô óùNnVlTÓ¡\Õ.
ùYiLXm (Bronze)
ùNmûTÙm, ùYsÂjûRÙm LXkÕùNnVlTÓm JÚ LXl× EúXôLm BÏm. £XNUVm ARàPu ÕjR SôLjûRÙm úNôójÕ®ú``Uô] RuûU EiPôdLlTÓ¡\Õ.
CRu ̈ \m £Ll× ØRp UgNs YûW AûUkÕCÚdÏm. CRu EÚÏ ¨ûX 1005oC. CÕ©jRû[ûV ®P L¥]Uô] EúXôLm. CûRªL áôóûUVô] LÚ®L°u êXm ÑXTUôLùU£²e ùNnV Ø¥Ùm. CRu ÕLsLs¡WôàXWôL CÚdÏm. ©Wj§úVLUô]ùYiLX AXôûV TVuTÓj§ ©úW£e WôhùNnVlTÓ¡\Õ. TpúYß LXûY ®¡Rj§pRVô¬dLlTÓm ùYiLXm TpúYßùTôÚsLs RVôôó ùNnV TVuTÓjRlTÓ¡\Õ.
LôÃVm Utßm ARu LXl× EúXôLeLs(Lead and its alloys)
LôÃVm CÚm×fNj§pXôR EúXôLj§pùTôÕYôL TVuTÓm EúXôLm BÏm.ùRô¯tNôûX«p TpúYß ®RUô]TVuTôh¥tÏ ETúVôLlTÓjRlTÓ¡\Õ.
LÄ]ô (Galena) Gu\ êXlùTôÚ°≠ÚkÕLôÃVm RôVôôó ùNnVlTÓ¡\Õ. LôÃVmL]UôL EúXôLm BÏm. CûREÚdÏmùTôÝÕ ùYs°ûV úTôußúRôt\m A°dÏm. CÕ ªÚÕYô]Õ UtßmúUp≠V©p RuûU ùLôiPÕ.A¬Uô]j§tÏ G§Wô]Õ. ¨ëdÏXôôóúWPVúN²p SpX CuÑúXhPWôLTVuTÓ¡\Õ. Npéôõd B£h UtßmûahúWô Ïú[ôôõd B£h úTôu\B£hLû[ G§ôódÏm RuûU ùLôiPÕ.
CÕ Lôôó úThPôõ«p TVuTÓjRlTÓ¡\Õ.úNôpPôó RVôôó ùNnV TVuTÓ¡\Õ. úUÛmCRu êXm ùT«ih RVôôó ùNnVlTÓ¡\Õ.
LôÃV AXônLs (Lead Alloys)
úT©h EúXôLm (Babbit metal)
úT©h EúXôLm LôÃVm, ùYsÇVm, ùNm×,Utßm Bi¥U¦«u LXlTôÏm. CÕªÚÕYô]Õ, EWônûY RÓdÏm. AR]ôXóCÕ úTôõe RVô¬dL TVuTÓjRlTÓ¡\Õ.
DVm Utßm ùYsÇVm LXl©p NôlhúNôpPo RVôo ùNnVlTÓ¡\Õ.
ÕjRSôLm Utßm ARàûPV AXônLs(Zinc and its alloys)
RLÓLs ÕÚ©¥dLôUp CÚdL ARu ÁÕÕjRSôL éfÑ ùTôÕYôL éNlTÓ¡\Õ.ERôWQj§tÏ CÚm× Yô°, ÕjRSôL áûWRLÓLs ØR≠V].
LôXûUu ApXÕ ©[ih Gu\êXlùTôÚs êXm ÕjRSôLm ¡ûPd¡\Õ.
CRu EÚÏ ¨ûX 420o C.
CÕ EûPVdá¥VÕ. ùYlTlTÓj§]ôpC[Ïm. CÕ úUÛm A¬Uô]j§tÏG§Wô]Õ. CjRuûU«u LôWQUôL úThPôõùLôsLXeLs RVôôó ùNnV Utßm áûWRLÓLÞdÏ úUtéfÑ éN TVuTÓjRlTÓ¡\Õ.
LôpYû]v ùNnVlThP CÚm×j RLÓLsÁÕ ÕjRSôLm éNlTÓ¡u\].
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.7.21
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64
ùYsÇVm Utßm ùYsÇV AXônLs(Tin and tin alloys)
ùYsÇVm (Tin)
Lô£hûWh (cassiterite) ApXÕ ¥u vúPôu(tinstone) êXm ùYsÇVm RVôoùNnVlTÓ¡\Õ úRôt\j§p ùYs° úTôußùYiûUVôL CÚdÏm Utßm CRàûPVEÚÏ ¨ûX 231o C. CÕ ªLÜm ªÚÕYô]ÕUtßm A§L A[Ü A¬Uô] G§ol×j RuûUùLôiPÕ.
EQÜ AûPdÏm CÚm× ¥uL°p úUpéfNôL TVuTÓ¡\Õ. úYß EúXôLeLÞPuLXkÕ AXôn RVôo ùNnVÜmTVuTÓjRlTÓ¡\Õ.
ERôWQm: ùYsÇVØm ùNm×m úNojRôpùYiLXm EÚYô¡\Õ, ùYsÇVØm DVØmúNojRôp úNôpPo (solder) EÚYôÏm.ùYsÇVm, ùNm×, DVm Utßm Bi¥U¦B¡VûYLû[ úNojÕ Tô©h EúXôLm (Babbit)RVôo ùNnVlTÓ¡\Õ.
AÛª²Vm (Aluminium)
AÛª²Vm JÚ Sôu ùToWv EúXôLm BÏm.CÕ TôdûNh (BAUXITE) Gu\ RôÕ ùTôÚ°pCÚkÕ RVôo ùNnVlTÓ¡\Õ. CÕ ùYsû[ApXÕ NômTp ̈ \m ùLôiPRôL CÚdÏm.CRu EÚÏ ̈ ûX 660o C. CÕ ªuNôWm Ut\mùYlTjûR G°§p LPjÕm RuûU EûPVÕ.CÕ ªÚÕYô]Õ, Utßm PdûPp (Ductile)RuûU ùLôiPÕ Ïû\kR CÝ®ûNùLôiPÕ, CÕ ®Uô]m EtTj§, UtßmúTl¬úL`u úYûX (Fabrication) B¡VCPeL°p TVuTÓjRlTÓ¡\Õ, Hù]u\ôpCÕ ªLÜm CúXNô] EúXôLm BÏm ªuùRô¯XLeL°Ûm RtùTôÝÕ A§L A[®pTVuTÓjRlTÓ¡\Õ. ÅÓL°ÛmùYlTlTÓjRdá¥V ùTôÚsL°pTVuTÓjRlTÓ¡\Õ.
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.7.21
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CÚm©tÏm, G@¡tÏm CûPúVVô] ®j§VôNeLs, LXl× G@Ï UtßmLôoTu G@Ï T«t£ 1.7.22
CÚm©tÏm, G@¡tÏm CûPúVVô] ®j§VôNeLs (Difference between iron and steel)
1 PôhPô AVou v¼p Àaôo
2 Ck§Vu AVou v¼p úU,YeLô[m
3 ®vúYvYWnVô LoSôPLôAVou v¼p
4 ©Xôn v¼p ©[ôuh Nj¾vLo
5 ÕoLôléo v¼p úU.YeLô[m©[ôuh
6 ApXôn v¼p úU.YeLô[m©[ôuh (ÕoLôéo)
7 ùTôdLôúWô v¼p Àaôo©[ôuh
8 ÚoúLXô v¼p J¬Nô©[ôuh
9 úNXm v¼p ©[ôuh RªrSôÓ
10 ®NôLlTh¥]m v¼p Bk§W©[ôuh ©WúRNm
Ck§Vô®pEs[CÚm× ùRô¯t NôûXLs
Y. CÚm× ùRô¯t Uô¨Xm Gi NôûX«u ùTVo
Y.Gi A¥lTûP CÚm× G@ÏúYßTôÓLs
1 AûUl× çV¨ûX CÚm× Utßm LôoTu B¡VYt\ôpEÚYô]Õ.
2 YûLLs Yôol× CÚm× LôoTu G@Ï Utßm LXl× G@ÏúR²Úm× Utßm G@Ï
3 ÕÚl©¥jRp G°§p Bd³úPNu TpúYß áßLs Es[RôpAûPRp Utßm ARu ÕÚl©¥jR≠ÚkÕ TôÕLôd¡\Õ.®û[YôL ÕÚl©¥lTÕ
4 ×\júRôt\m ÕÚl©¥jÕm, ùNôW T[T[lTôL CÚdÏm.ùNôWlTôLÜm CÚdÏm
5 ETúVôLm Lh¥PeLs, LÚ®Ls Lh¥PeLs, LôoLs, W«púYUtßm Rô²Ve¡L°p Utßm Rô²Ve¡L°p
6 ¡ûPjRp CVtûL«p ¡ûPd¡\Õ EÚYôdLlTP úYiÓm.
1 CÚm× NjÕ A§Lm C§p CÚm× NjÕ ¡ûPVôÕ
2 CRu EÚÏ ̈ ûX EÚÏ ̈ ûX Ïû\ÜA§Lm
3 CRu ̈ \m LÚl× CÕ TpúYß ̈ \eL°pApXÕ ©WÜu CÚdÏm
4 ÕÚ ©¥dÏm ÕÚ ©¥dLôÕ
5 LôkRjRuûUûV LôkRjRuûUûV HtTÓjR Ø¥Ùm HtTÓjR Ø¥VôÕ
6 Ï°okR ̈ ûX«p CÕ ùYlT ̈ ûX«pùSôßeÏm RuûU ùSôßeÏm RuûUùLôiPÕ ùLôiPÕ
CÚm×fNjÕs[ CÚm×fNj§pXôREúXôLm EúXôLm
1 LôoTu A§Lm LôoTu Ïû\Ü
2 LôoTu R²jÕ CÚdÏm LôoTu LXkÕ CÚdÏm
3 EÚÏ ̈ ûX Ïû\Ü EÚÏ ̈ ûX A§Lm
4 LôkR RuûUûV LôkR RuûU HtTÓjRHtTÓjR Ø¥VôÕ Ø¥Ùm
5 ùSôßeÏm RuûU CûR úTôo_ó ùNnVEs[Rôp CûRúTôo_ó Ø¥ÙmùNnVØ¥VôÕ
6 G°§p ÕÚ ©¥dLôÕ G°§p ÕÚ ©¥dÏm
7 CûR ùYpÓ CûR ùYpÓ ùNnVùNnVØ¥VôÕ Ø¥Ùm
Yôol× CÚm×dÏm G@ÏdÏm Es[ ®j§VôNm
Yôol× CÚm× G@Ï
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Yôôól× CÚm×, ªÚÕ G@Ï, Utßm G@Ï B¡VYt±u RuûULû[ Jl©ÓRp(Comparison of the Properties of Cast Iron, Mild Steel and steel)
êXl 2 ØRp 4.5% LôôóTu 0.1 ØRp 0.25% LôôóTu 0.5 ØRp 1.7% LôôóTuùTôÚhLs(Composition)TXm (Strength) – CßdÏ ®ûN A§Lm – CßdÏ ®ûN – CßdÏ®ûN
SÓjRWUô]Õ A§Lm– CÝ ®ûN Ïû\Ü – CÝ ®ûN – CÝ ®ûN A§Lm
SÓjRWUô]Õ– ùYhÓ ®ûN Ïû\Ü – ùYhÓ ®ûN A§Lm – ùYhÓ®ûN A§Lm
úUp≠V©≠h¥ Ïû\Ü A§Lm A§Lm (malleability)
Pd¥≠h¥ Ïû\Ü A§Lm A§Lm (ductility)
L¥]jRuûU SÓjRWUô] L¥]j ªÚÕjRuûU L¥]jRuûU (hardness) RuûU Utßm L¥]j
RuûUdLô] ùYlTA[®tÏ ùYlTlTÓjRlThÓ L¥]lTÓjRlThÓ ÏûYuf (Quench)ùNnVlTÓ¡\Õ
§iûUj RuûU Ïû\Yô] §iûUj §iûUjRuûU LôôóTu A[ûYl(toughness) RuûU A§LUôL CÚdÏm ùTôÚjÕ §iûUj
RuûU UôßTÓm
ùSôßeÏm ùSôßeÏm úUp≠V©p úUp≠V©pRuûU (Brittleness)úTôôó_õV©≠h¥ úTôôó_ó ùNnV CVXôÕ úTôôó_ó ùNnV Ø¥Ùm úTôôó_ó ùNnV Ø¥Ùm(Forgeability)ùYpP©≠h¥ ÑXTUôL Tt\ ûYdL ÑXTUôL Tt\ ûYdL Tt\ ûYdLXôm
(Weldability) Ø¥VôÕ Ø¥Ùm
Yôôól× ÑXTUôL Yôôól× ÑXTUôL Yôôól× Yôôól× ùNnV(Casting) ùNnV Ø¥Ùm ùNnV CVXôÕ Ø¥Ùm
Áh£VpRuûU Ïû\Ü A§Lm A§Lm(Elasticity)
RuûULs Yôôól× CÚm× ªÚÕ G@Ï G@Ï
EúXôLm Utßm AúXôLj§u úYßTôÓLs
EúXôLm AúXôLm
T[T[lTôL T[T[lTôLCÚdÏm CÚdLôÕ
ªuNôWjûRÙm ªuNôWjûRÙmùYlTjûRÙm ùYlTjûRÙmSu\ôL LPjÕm G°§p LPjRd á¥VûY
ApX
ùTÚmTôÛm PdûPp RuûUPdûPp RuûU ¡ûPVôÕEûPVÕ
J° FÓÚYôÕ ùUp≠V RLPôLCÚkRôp J° FÓÚÜm
úUp≠V©p RuûU §PlùTôÚ[ôLA§Lm CÚdÏmùTôÝÕ
EûPkÕ®Óm
ApLûXu A£¥d BdûNPôLBdûNPôLUôßm Uôßm
J≠ GÝlTd á¥VÕ J≠ GÝlTôÕ(U¦ûV A¥dÏmùTôÝÕ HtTÓmJ≠ûVl úTôp)
ùTôÕYôL 1 ---- --- 3 ùTôÕYôL 4 ----- - - 8úYXu£ GXdhWôu úYXu£ GXdhWôuùLôiPÕ ùLôiPÕ
ùTÚmTôÛmÑXTUôL ÕÚ©¥dÏm
ùTôÕYôL EÚÏ ̈ ûXA§Lm(ùTôÕYôL §PlùTôÚs Aû\«uùYlT ̈ ûX«p(TôRWNm R®W)
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.7.22
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CWlTo, UWm Utßm CuÑúXh¥e ùTôÚsLÞdLô] RuûULs UtßmETúVôLeLs T«t£ 1.7.23
CWlT¬u RuûULs UtßmETúVôLeLs (Properties and uses of rubber)
WlTo (Rubber)
CÕ Áh£j RuûUÙûPV ùTôÚ[ôÏm. CûRCqYô\ôL YûLlTÓjRXôm.
• CVtûL WlTo
• L¥] WlTo
• ùNVtûL WlTo
CVtûL WlTo (Natural rubber)
CÕ RôYWeLû[ ©¬jùRÓjRp êXm¡ûPd¡\Õ. ùYlTlTÓjÕmùTôÝÕC[Ïm. CÕ, 30°C -p. JhÓm RuûUÙPàm,5°C -p. L¥]UôÏm RuûU ùLôi¥ÚdÏm.
NpTo WlTÚPu úNodLlThÓ AkR áhÓlùTôÚs ùYlTlTÓjRlTÓ¡\Õ. CkRùNVpØû\ûV YpLû]£e GußAûZd¡ú\ôm. CkR ùNVp Øû\«u êXmY≠ûUVô], L¥]Uô] Utßm A§L¨ûXjRuûUÙûPV WlTo ¡ûPdÏm. úUÛmùYlT Uôt\j§]ôp Tô§dLlTPôUÛmUtßm BoLô²d LûWN≠p LûWVôUÛmCÚdÏm. ARu RhT ùYlTj RuûUûVA§L¬lTRu LôWQUôL Bd£úPNu ªLÜmÏû\dLlThÓ ®Ó¡\Õ.
LÚl× LôoTu, B«p ùUÝÏ UtßmTXYtû\ úNolTRu êXm EÚYUôt\mHtTÓjÕm RuûULs Ïû\dLlTÓ¡\Õ.WlTo DWj RuûUûV RôeLd á¥VÕ Utßmªu LPjRÛdÏ G§Wô] SpX RuûULsùLôiPÕ. CRu Ød¡Vj ¾ûULs ¸úZùLôÓdLlThÓs[Õ.
• ùThúWô≠Vm GiûQdÏ G§Wô] Ïû\kRRûP Es[Õ.
• ã¬V J° TÓmT¥ ûYdLd áPôÕ.
• A§L ªu AÝjRØs[ LPj§L°pCuÑúXN]ôL TVuTÓjRd áPôÕ.
• Ïû\kR ùYlT¨ûX ùNVp Øû\L°pTVuTÓj§]ôp, AÕ 60°C ùYlT¨ûX«pùY¥l× HtTÓRp Utßm EûPRp HtTÓm.
• ùNm×Pu, WlT¬p Es[ NpTo úY§®û] ׬YRôp TVuTÓjÕm ùNm×d Lm©ùYsÇVm éNlTh¥ÚdL úYiÓm.
L¥] WlTo (Hard rubber)
NpT¬u A[®û] WlT¬p A§L¬lTÕUtßm ¿iP úSWm YpLû]£e ùNnYÕB¡VYt\ôp WlTo, L¥] WlTo BLUô±®Óm. CRû] GúTôû]h GußmAûZd¡ú\ôm. CÕ SpX ªu Lôl× RuûUUtßm CVk§W®Vp RuûU EûPVRôLCÚdÏm.
ETúVôLeLs (Uses)
CÕ úThP¬ LuùPn]oLs, úT]púTôoÓLs, ×xμe, GúTôû]h ¥ë×LsUtßm TXYtû\ RVô¬dLl TVuTÓ¡\Õ.
ùNVtûL WlTo (Synthetic rubber)
CÕ CVtûL WlTo úTôuú\ Es[RôÏmUtßm CÕ ùRoúUô ©[ôv¥d ®û]p ûaTô≠Uo -«≠ÚkÕ ¡ûPdLl ùTß¡\Õ.Ød¡VUô] ùNVtûL WlToL[ôY]:
• ûShûWh ×hPô¥u WlTo
• ×ëûPp WlTo
• ûaTXôu WlTo
• ¨úVôl¬u WlTo
• £≠dLôu WlTo
Y. ùTVo RuûULs ETúVôLeLsGi
1 ûShûWh SpX ®¬§\u, úRnUô]jûR BhúPôùUôûTp PV¬às×hPô¥u WlTo G§odÏm RuûU, Ïû\kR Es[ ¥ë×Ls
ùYlT¨ûX«p Yû[kÕùLôÓjRp, ¿iP BÙs,Bd£úPNu, Ïû\kR CÝY≠ûU, ûadúWôv úLôl©£h¥.
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Y. ùTVo RuûULs ETúVôLeLsGi
2 ×ëûPp ùThúWô≠Vm GiûQ úLv ãPô] Utßm Ï°of£Vô]Utßm BpLaôp LûWN≠]ôp ¨ûX«p úPl×L[ôL ¬lúToTô§dLlTÓm. CÕ ùYlTm Utßm ùNnÙm ùTôÝÕ TVuTÓjRlBd£úPN]ôp Tô§dLlTPôÕ TÓ¡\Õ. Utßm JúNô²tÏ A§LTô§lûTRWôÕ.
3 ûaTXôu ã¬V J° Utßm 150°C YûW Es[ ªu JVoLs Utßm úL©sLÞdÏWlTo ùYlT ̈ ûX«]ôp Tô§lTûPVôÕ úUp LYNUôL TVuTÓjRl
TÓ¡\Õ.
4 ¨úVôl¬u ¿iP BÙs, Bd£úPNu Utßm JVoLÞdÏ CuÑúXNu BLÜm,WlTo YôÙ®]ôp Tô§dLlTPôRÕ, SpX úL©sLÞdÏ Lôl× Eû\VôLÜm
ùYlTd LPjRûX RôeLd á¥VÕ, (LYNUôLÜm) TVuTÓjRlTÓ¡\ÕUtßm ùSÚlûT RôeLd á¥VÕ,Ïû\kR CVk§W®Vp RuûULsEûPVÕ.
5 £≠dLôu EVokR ùYlT¨ûX«p ùNVpTÓRp TYoúL©ÞdÏ CuÑúXN]ôLÜm(200°C), Yû[kÕ ùLôÓdÏm RuûU, Utßm FÕ EûX úLôd KY²uDWjRuûU Utßm A¬Uô]j§tÏ LhÓlTôhÓ JV¬Ûm, G@ÏG§Wô] RuûU, Bd³úPNàdÏ BûXLs Utßm AÔªu ¨ûX-G§Wô] RuûU, KúNôu, Bod¡e VeL°Ûm, ûa ©¬dÏYu£(arcing), SpX LPjRôjRuûU Utßm ù_]úWhPoL°Ûm, ùLô§LXu,ùYlTm LPjRôûU. CÕ JÚ £\kR ®Uô] ¨ûXV ®[dÏLs UtßmCuÑúXhPo BÏm. ¡úWuLÞdÏ TVuTÓjRlTÓ¡\Õ
UWj§u RuûULs Utßm TVuLs(Properties and uses of timber)
ùTôÕYô] RuûULs (General properties)
UWm ¸rLiP RuûULû[ ùLôi¥ÚdLúYiÓm.
• úSWô] SôoLs (A) CûZLs
• ©ú[²e ùNnÙm ùTôÝÕ ThÓlúTôußùUuûUVôL CÚdL úYiÓm.
• JúW Uô§¬Vô] YiQm.
• JÝeLô] YÚPYû[VeLs.
• Í®]v (Heaviness).
• LômTôdh UôÓX¬ L§oLs UtßmEߧVôL JÚe¡ûQkR SôojRuûU.
• C²ûUVô] UQm.
• ©ûQl× CpXôR, Ø¥fÑLs At\ RuûU.
• úUp TWl× T[T[lTôLÜm UtßmYô°]ôp ùYhÓm ùTôÝÕ ARu TtLs£dLôUp CÚdÏm YiQm CÚjRp.
YûLLs (Classification)
• UWeLs ¸rLiPYôß YûLlTÓjRlThÓs[].
a ùUuûUVô] UWm (Softwood)
b L¥]Uô] UWm (hardwood)
ùUuûUVô] UWm (Softwood timber)
• ùTôÕYôL F£ûVlúTôp ùU≠RôL Es[CûXLû[ EûPV UWeLs ùUuûUVô]UWm Gußm ALXUô] CûXLû[ EûPVUWeLs L¥]Uô] UWeLs G]ÜmA±VlTÓ¡u\].
• CkR UWm ùW£u Utßm PoTuûPuEs[RôL CÚdÏm.
• CkR UWm ùUuûUVô] UQm ÅÑmUWUôL CÚdÏm.
• SôoLs úSWôL CÚdÏm.
• AûUl× ùUuûUVôLÜm ùTôÕjRuûUùLôiPRôLÜm CÚdÏm.
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.7.23
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69
• CÝjRûLûY G§olT§p EߧVôLCÚdÏm.
• SôoLÞdÏ CûPúV TXÅ]UôL CÚdÏm.
• YÚP Yû[VeLs ®j§VôNUôL, ARôYÕJÚ TdLm ùUuûUVôL, ÖiÕû[LsUtßm ùY°¬V YiQjÕPuLôQlTÓm, B]ôp Utù\ôÚTdLmAPoj§VôLÜm Utßm AÝjRUô]YiQjÕPu CÚdÏm.
• ùTôÕYôL UWj§u YiQm ùY°¬Ùm(A) ûTu vlìv, @©o, Bx, ûLp,¥úVôPo Utßm TXYôL CÚdÏm.
L¥]Uô] UWj§u RuûULs (Properties ofhardwood)
• CqYûL ùTôÕYôL A§L NRÅRAªXjûRd ùLôi¥ÚdÏm.
• T°fùNu\ YiQj§p CÚdÏm.
• YÚP Yû[VeLs ®j§VôNUôL CÚdLôÕ.
• C§p úYûX ùNnYÕ L¥]UôL CÚdÏm.
• CÕ ùYhÓjRûLûY G§odÏm RuûUEûPVÕ.
• SôoLs Juû\Juß ©u²dùLôi¥ÚdÏm.
• CÕ ùTôÕYôL APoj§Vô]YiQeL[ô] ©WÜu, Kd, YôpSh, ¼d,UaôúLô², ºμm, Tô×p, Nôp UtßmTXYtû\d ùLôi¥ÚdÏm.
ETúVôLeLs (Uses)
ùUuûUVô] UWm (Soft timber)
• U≠Yô]j RuûU LôWQUôL U≠Ü YûLÅÓLÞdÏ LRÜLs, Nu]pLs, Aû\LXuLs RVô¬dLl TVuTÓ¡\Õ.
• G¬ùTôÚ[ôL ETúVôLl TÓjRlTÓ¡\Õ.
• £X UWeLs áûPLs Utßm ®¬l×LsRVô¬dL TVuTÓjRlTÓ¡\Õ.
• CRu ThûP £X CPeL°p BûPVôLTVuTÓjRlTÓ¡\Õ.
L¥]Uô] UWm (Hard timber)
• EVoRW Aû\LXuL[ô] SôtLô≠Ls,úUûNLs, úNôTôdLs, §YôuLs, TÓdûLAû\ Lh¥pLs Utßm TXYtû\RVô¬dLl TVuTÓjRlTÓ¡\Õ.
• EVoRW ÅÓLÞdÏj úRûYVô] Tô≠x,ùT«u¥e RuûUdÏ Ht\ YûL«pLRÜLs, Nu]p NhPeLs RVô¬dLTVuTÓjRlTÓ¡\Õ.
• LRô (katha) RVô¬dL TVuTÓjRlTÓ¡\Õ.
ªu CuÑúXhPWôL UWm (Wood as anelectrical insulator)
• CuÑúXhPWôL ETúVôLlTÓjRCmUWj§u FúP GiûQ (A )©\ùTôÚsLs Eh×Ïj§ TVuTÓjÕRp
ERôWQm.
• ªuNôW CVk§WeL°p ûYi¥e¡tÏCûPúV ûYdLlTÓm vXôh ùYh_v(slot wedges) BL TVuTÓjRlTÓ¡\Õ.
CuÑúXh¥e ùTôÚsLs (Insulatingmaterials)
®[dLm (Description)
CqYûL ùTôÚsLs ªuú]ôhPjûRØÝûUVôLúYô (A) A§LThNUôLúYôRÓdÏm RuûU EûPVÕ. (LPjRôjRuûU)CkR A§LThN RûPjRuûU ùTôÕYôL ùUdKm -p CÚdÏm 1 L]. ùNÁdÏ (1 ùUd Km =106 KmLs) BL CÚdÏm. ûP GXdh¬d(dielectric) Eߧ EûPVRôL CÚdÏm. CRu®[dLm Gu]ùY²p EVo ªu AÝjRmTVuTÓjRlTÓm ùTôÝÕ ùLôÓdLlThPR¥Uu Lôl× ùTôÚs EûPVúYô (A)TXÅ]m AûPVúYô ùNnVôÕ.
CuÑúXhP¬u RuûULs (Properties ofinsulators)
JÚ SpX CuÑúXhPo ùTôÚÞdÏúRûYVô]ûY CûY:
• ûa vùT£@©d ùW£vhuv (High specificresistance) ùUd Km/L] ùNÁ CÚdÏm. CÕªu CZlûTd ªLd Ïû\kR A[®tÏùLôiÓ YÚm.
• SpX ûPGXdh¬d EߧjRuûU (Gooddielectric strength) ARôYÕ ©úWdPÜu ªuAÝjRj§u EVokR ThNm (¡úXôúYôph/ªÁ -p ùY°lTÓjÕm).
• SpX CVk§W®Vp EߧjRuûU, CݨûX(A) AÝjR¨ûX (¨ßÜm úSWj§p UtßmúYûXf ãZ≠p HtTÓm) RûLûYjG§odÏm §\u).
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.7.23
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• ùYlT¨ûX EVÚm ùTôÝÕ ̈ ûXûU ªLÏû\kR ¨ûX«p Tô§lTûPRp(CuÑúXh¥e RuûU EVoùYlT¨ûX«]ôp A§Lm Uô\ô§ÚjRp)ARôYÕ ªu NôR]eLû[ ØÝûUVôLCVdL ¨ûX«p ûYj§ÚdÏm ùTôÝÕTô§lTûPVô§ÚjRp BÏm.
• Y°UiPX DWlTRUô] ãr¨ûX«p DWmE±gNôR RuûU (Ïû\kR A[ÜDWjRuûU E±gNlThPôÛm,CuÑúXhP¬u RuûULs ϱlTôLvùT£@©d ùW£vPuv (specific resistance)Utßm ûP GXdh¬d EߧjRuûUϱl©hP A[Ü Ïû\kÕ ®Óm Yônl×A§Lm) úYiÓm.
CuÑúXhPoLs ªu Õû\«p TVuTôÓ
1 ûUdLô ûYi¥e¡p (vXôh CuÑúXN]ôL)
2 WlTo JVoL°p CuÑúXN]ôL
3 EXokR TÚj§ ûYi¥e
4 Yôo²x ûYi¥e
5 BvùTpPôv Cv§¬ùTh¥, ùLh¥pLs B¡VYt±u A¥lTôLj§p
6 ÏhPô TôofNô (Gutta ¿oêr¡ úL©sLsparcha)
7 ÀeLôu úUp¨ûX ªu Lm©LÞdÏ CûP«Xô] CuÑúXhPoLs
8 LiQô¥ -do-
9 EXokR UWm úUp ¨ûX ªu Lm©Lû[ RôeÏm ÏßdÏ
10 ©Vôv¥d Ñ®hÑL°u EPpTϧ (A) JVoL°u CuÑúXNu
11 GúTôû]h ªu Uôt±«u Tô©u
12 @ûTTo Tô©u RVô¬dL Utßm ûYi¥e CuÑúXhPWôL
13 GmTVo ¡[ôj ûYi¥e CuÑúXhPWôL
14 ùXRWônÓ úTlTo -do-
15 ªp≠úUdv úTlTo -do-
16 ©.®.£ JVo CuÑúXhPWôL
17 úTdûXh Ñ®hÑLs RVô¬dL Utßm CuÑúXhPWôL
18 ù`pXôd -do-
19 vúXh úT]p úTôoÓ RVô¬dL
20 TôW@©u ùUÝÏ AûPdL
RVô¬l×Ls Utßm CuÑúXhPoLs (Products and insulators)
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.7.23
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¨û\, ¨û\«u AXÏLs, APoj§ Utßm GûP T«t£ 1.8.24
m - ùTôÚ°u ¨û\
g - ×®Dôól× ®ûNVôp HtTÓm ØÓdLmÁhPôó/®]ô¥2 = 9.81 m/sec2
V - ùTôÚ°u TÚU A[Ü
ρ - APôój§ (‘úWô’ G] EfNôõdLÜm')
W ApXÕ FG - GûP ApXÕ GûP ®ûN
¨û\ (Mass) (TPm 1)
JÚ ùTôÚ°p APe¡Ùs[TÚlùTôÚhL°u §¦Ü ¨û\ G]lTÓm¨û\«u AXÏ F.P.S Øû\«p TÜiÓ (lb)C.G.S. Øû\«p ¡Wôm (gr) M.K.S Utßm S.IØû\«p ¡úXô ¡Wôm £XNUVeL°p 1 PuGuTÕ 1000 ¡.¡WôUôL ETúVôLlTÓjRlTÓm.Kôó AX¡p CÚkÕ úYß JÚ AX¡tÏ Uôt\1000 LôW¦VôL TVuTÓ¡\Õ.UôtßmùTôÝÕ êu\ôYÕ RNU ×s°dÏUôt\Üm. ERôWQm 1 Pu = 1000 ¡úXô ¡Wôm1 ¡Wôm = 1000 ªp≠ ¡Wôm.
APôój§ (Density)
KWXÏl TÚUàs[ ùTôÚ°u GûP APôój§G]lTÓm. CRàûPV AXÏLs ¡Wôm/ùN.Á3
ApXÕ ¡.¡/ùP£.Á3 ApXÕ Pu/Á3.
APôój§ =
GûP (Weight) (TPm 2)
JÚ ùTôÚ°u ÁÕ ùNVtTÓm 骫u ûUVmúSôd¡V ×® Dôól× ®ûN GûP G]lTÓm.ùTôÚ°u ¨û\ Utßm ×®Dôól× ®ûNVôp
HtTÓm ØÓdLj§u ùTÚdÏ ùRôûL GûPG]lTÓm ùTôÚ°u GûP CPj§tÏ CPmUôßTôÓm.
GûP = W ApXÕ FG = ̈ û\ x ×®Dôól× ̈ ûXGi
= m x g
Øû\ ¨TkRû] YûWVß A[ÜAt\ AXÏ dLlThP Uôt\m
AXÏLs
©¬h¥v 1 TÜiPp 1 TÜih 32.2 TÜiPp Øû\ GûP (1lbx1ft/sec2
F.P.S. = 1TÜiPp)
ùNh¥ 1 ûPu 1¡Wôm 981 ûPuv ÁhPo GûP ¡Wôm 1gm x1cm/sec2
®]ô¥ Øû\ C.G.S. ÁhPo ¨ëhPu 1.¡.¡ GûP 1 ¨ëhPu = ¡úXô ¡Wôm ®]ô¥ = 1¡,¡x1Á/
®]ô¥2
Øû\ M.K.S. A¡X ¨ëhPu ¨ëhPu -do- EXL RW ̈ oQV Øû\ S.I.
1 ¡úXô GûP = 9.81 ¨ëhPu1 ¨ëhPu = 105 ûPuv( úRôWôVUôL 10¨ëhPu)
¨û\
TÚU A[Ü
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¨û\ Utßm GûPdÏ CûPúVVô] ®j§VôNm, APoj§ UtßmAPoj§ GiÔdÏ CûPúVVô] ®j§VôNm T«t£ 1.8.25
¨û\ Utßm GûPdÏ CûPúVVô]®j§VôNm (Difference between mass and weight)
Y. ¨û\ GûPGi
1 TÚlùTôÚ°u ×® Dol× ®ûNVôp§¦Ü APe¡ DodLlTÓ¡\ÕEs[Õ
2 GkR CPj§Ûm CPj§tÏ HtT¨û\ Uô\ôÕ UôßTÓm
3 ùTôÚ°u ̈ û\ ×®Dol× ®ûNé_ó_÷VUôL CpûXùV²pCÚdLôÕ. GûP é_ó_õVUôL
CÚdÏm
4 CVp©Vp ®p RWôûNdRWôûNd ùLôiÓ GûPûVdùLôiÓ LQd¡PXôm¨û\ûVdLQd¡PXôm
5 vúLXôo ùYdPôoÏYôi¥h¥ ÏYôi¥h¥
6 ¿¬p êrL ¿¬p êrLûYlTRu êXm ûYlTTRu êXm¨û\ Uô\ôÕ ùTôÚ°u GûP
UôßTÓm
7 CRu AXÏ CRu AXÏ¡Wôm Utßm ¡úXô¡Wôm GûP¡úXô¡Wôm «p CÚdÏm,BÏm ®ûN«u AXÏ
¨û\ Utßm GûP ùYqúYßTôõUôQm ùLôiPÕ
ùTôÚ°u¨û\=TÚU A[Ü xAPôój§
GûP = ¨û\ x×®Dol× ®ûN«]ôp HtTÓmØÓdLm
GûP,APôój§ Utßm APôój§ Gi
TÚlùTôÚ°u §¦Ü GûPVôp UhÓmA[dLlTÓ¡\Õ. TÚU A[®u ϱl×CpXôUp A[dLlTÓ¡\Õ. DVØmAÛª²VØm NU GûPVôL CÚkRôÛmDVj§u TÚU A[ûY Jl©ÓmùTôÝÕAÛª²Vj§u TÚU A[ûY ®P DVj§uTÚU A[Ü Ïû\YôL CÚdÏm.ClùTôÝÕSôm ùNôpXXôm. ARôYÕ AÛª²Vj§uAPôój§ûV ®P DVj§u APôój§ A§LmARôYÕ úYßYôô ójûR«p ùNôpXúYiÓUô]ôp AÛª²VjûRd Lôh¥ÛmDVj§u APôój§ A§Lm. (TPm 1 & 2)
¨û\dÏm TÚU A[ÜdÏm Es[ùRôPôó×Rôu APôój§ G]lTÓ¡\Õ.
TÚU A[®u ̈ û\ûVjRôu APôój§ GußùNôpXlTÓ¡\Õ. ERôWQm JÚ L] ùP£ÁhPôó Ri½ôõu ¨û\ JÚ ¡úXô ¡WômBÏm. ClT¥VôL APôój§Vô]Õ 1 ¡úXô /ùP..Á3 BÏm.
AXÏ
APoj§ ¸rLiPYôß A[dLlTÓ¡\Õ.
MKS/SI= Kg/m3, CGS - 1 gm/CC FPS–Lbs/Cft
§Pl ¡Wôm/ §WYe ¡Wôm/ùTôÚs L] ùN.Á Ls L ùN.Á
1 AÛª²Vm 2.7 Ri½o 1.00
2 DVm 11.34 ùThúWôp 0.71
3 Yôol× 6.8 to 7.8 Bd£_u 1.43CÚm×
4 G@Ï 7.75 to ¼Np 0.838.05 GiùQn
TÚlùTôÚ°u APôój§ Gi JlTPôój§Gußm AûZdLlTÓ¡\Õ.
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ãj§Wm
APôój§ Gi ApXÕ JlTPôój§
APôój§ Gi =ùTôÚ°u ̈ û\
4°C p AúR TÚUàs[ ¿¬u¨û\
JÚ ùTôÚ°u APoj§ GuTÕ JWXÏT Ú U à s [A l ù T ô Ú ° u¨û\VôÏm.
CRu AXÏ ¡Wôm/ùN.Á 3, TÜih/L]A¥,Utßm ¡úXô/L.Á
JÚ ùTôÚ°u APoj§ Gi GuTÕ AlùTôÚ°u APoj§dÏm 40C ¿¬uAPoj§dÏm Es[®¡RUôÏm.CRtÏ AXÏLs¡ûPVôÕ, GiU§lTôp UhÓúUá\lTÓm.
JlTPoj§ =APoj§ =
¨û\
TÚU A[Ü ùTôÚ°u ¨û\
AúR TÚUàs[40C«p Es[ ¿¬u¨û\
úUtá±V AhPYûQ«p CÚkÕ, SômùLôÓdLlThP TÚU A[®u GûPûV (¼NpGiùQn) GkR AX¡Ûm TÚlùTôÚ°uAPôój§ Gi LôQXôm. AúR Uô§ôõ L]A[ûYÙm LiÓ©¥dLXôm.
APoj§dÏm Utßm APoj§ Gi(JlTPoj§ ) CûPúVVô] JlÀÓComparison Between Density And Specific Gravity(Relative Density)
APoj§ JlTPoj§ (A)APoj§ Gi
§PlùTôÚs APoj§ §WYm APoj§Gi Gi
1 AÛª²Vm 2.72 ùThúWôp 0.71
2 DVm 11.34 úThP¬ 1.2 toB£h 1.23
3 Yôol× 6.8 to Ri½o 1.00CÚm× 7.8
4 G@Ï 7.82 ¼Np 0.83GiùQn
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.8.25
JWXÏ TÚUàs[ ùTôÚ°u ¨û\
4°C «p Es[ JWXÏ TÚUàs[ ¿¬u¨û\
=
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¨û\, GûP Utßm APoj§ B¡VYtßdLô] ùRôPo× LQdÏLÞm§\]ônÜ T«t£LÞm T«t£ 1.8.26
ERôWQm
• JÚ ùNqYL G@Ï RLh¥u A[ÜLs 220 x330 x 15 ª.Á CRu ¨û\ûV LQd¡Ó.(TPm 1) G@¡u APoj§ = 7.82 ¡Wôm/ùNÁ3
¨û\ = TÚU A[Ü x APoj§
= 22 x 33 x 1.5cm3 x 7.82 gm/cm3
= 1089 cm3 x 7.82 gm/cm3
¨û\ = 8.516 kg
Ri½¬u ̈ û\ = TÚU A[Ü x Ri½¬uAPoj§ = 250 ùP..Á3 x 1 ¡úXô / ùP . Á3
= 250 ¡úXô
GûP ®¬Ü = ̈ û\ x ×®Dol× ®ûN«]ôpHtTÓm ØÓdLm.
= 250 ¡ 10 Á/®]ô¥2
= 2500 ¡úXô.ÁhPo / ®]ô¥2
= 2500 ̈ ëhPu (1 ¡.¡ ÁhPo/®]ô¥2=1N)
3 15 ûPu ®ûNVô]Õ, ¨û\ `m' ÁÕùNÛjRlTÓ¡\Õ. CR]ôp 2.5 ùN.Á /®]ô¥2 -dÏ ØÓdLm HtTÓ¡\Õ. ̈ û\ûVLiÓ©¥.
1 ×ÜDol× GûP = 981 ûPu
15 ûPu = Gr.wt
®ûN = ̈ û\ x ®ûN«]ôp HtTÓm ØÓdLm
Gr.wt = ¨û\ x 2.5 ùN.Á/®]ô¥2
¡Wôm ùN.Á/®]ô¥2
= ¨û\ x 2.5 ùN.Á/®]ô¥2
¨û\ = ¡Wôm
= 0.00612 ¡Wôm
4 2 ¨ëhPu ®ûN 10 ¡úXô ¨û\«u ÁÕùNÛjRlTÓ¡\Õ ¨û\«u ÁÕùNÛjRlThP ®ûN«]ôp HtTÓmØÓdLjûR LiÓ ©¥.
®ûN = 2 ¨ëhPu ( 1 N = 1 ¡.¡/®]ô¥2)
®ûN = ¨û\ x ØÓdLm
2 ¡úXô ÁhPo / ®]ô¥2 = 10 ¡úXô xEtTj§Vô] ØÓdLm
2 x 1 ¡.¡ ÁhPo/®]ô¥2 = 10 kg xEtTj§Vô] ØÓdLm
EtTj§Vô] ØÓdLm= ÁhPo/®]ô¥2
= 0.2 ÁhPo/®]ô¥2
2 JÚ úNªl× Tôj§Wj§u Ri½oùLôs[Ü 250 ≠hPo ARàûPV GûPûV¨ëhP²p á\Üm. Ri½o Tôj§WmTWl©u ÁÕ ûYdLlThÓs[Õ (TPm 2)
(1 ≠hPo ¿¬u GûP = 1 ¡.¡Wôm ¿¬uGûP)
Ri½¬u APoj§ ¡Wôm / ùN.Á3 (ApXÕ)¡úXô / ùP . Á3
×®Dol× ®ûN«]ôp HtTÓmØÓdLm 10 Á/®]ô¥2 (úRôWôVUôL)
ùLôs A[Ü = 250 ≠hPo = 250 ùP . Á3
TÚU A[Ü
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5 JÚ ¡úXô ¨û\ Es[ JÚ ùTôÚ°uGûPûV LQd¡ÓL. AR]ûPV ×®Dol×®ûN«]ôp HtTÓm ØÓdLm = 1 ¡úXô x9.81 ÁhPo/®]ô¥2
(1 ¡úXô ÁhPo / ®]ô¥2=/ ̈ ëhPu)
@ 9.81 ¡úXô ÁhPo / ®]ô¥2
= 9.81 ̈ ëhPu
Uô§¬ ¾o®p ‘g’ «u U§l× 10 ÁhPo/®]ô¥2 G] GÓjÕd ùLôs[lThÓs[Õ. ϱl©hÓ GÕÜmá\®pûX Gu\ôp CqYôßGÓjÕd ùLôs[Xôm.
.• ùYtß úLô[j§u ùY°l×\ UtßmEh×\ ®hPeLs Øû\úV 150 Utßm 70ª.Á CRu ¨û\ûV LiÓ ©¥ClùTôÚ°u APoj§ 7.5 ¡Wôm/ùN.Á3
(TPm 3)
6 JÚ Lô¬u ¨û\ 800 ¡úXô. ARàûPV®ûN GûPûV LiÓ©¥ (9.81 Á/®]ô¥2
G] GÓjÕd ùLôs[Üm)
( 1 ¨ëhPu = 1 ¡¡.ª/ùNÁ2)
Lô¬u ®ûN GûP = Lô¬u ¨û\ x ×®Dol×®ûNVôp HtTÓm ØÓdLm
= 800 x 9.81 ¨ëhPu
= 7848 ̈ ëhPu
7 JÚ EÚû[ Y¥Yô] ùRôh¥«u ®hPm2 ÁhPo ARu BZm 3.5 ÁhPo C§pùThúWôp ¨WlThÓs[Õ ùThúWô≠uGûPûV Pu²p LiÓ ©¥dLÜmùThúWô≠u APoj§ 720 ¡¡/Á3. (TPm 4)
¨û\ = TÚU A[Ü x APoj§
= TÚU A[Ü x 7.5 ¡/ùNÁ3
D= 150 ªÁ = 15 ùNÁ R= 7.5 ùNÁ
d = 70 ªÁ = 7 ùNÁ r = 3.5 ùNÁ
úLô[j§u TÚU A[Ü =
=
=1587.5 cm3
¨û\ = TÚU A[Ü x APoj§
= x 7.5
¨û\ = 1587.5 ùNÁ3 X 7.5 ¡Wôm/ùNÁ3
= 11906.6 ¡Wôm =11.9 ¡¡ = 12 ¡¡ (ùNôpXXôm)
ùRôh¥«u TÚUA[Ü
= 3.14 x 3.5 m3 = 10.99 m3
JÚ L]ÁhPo = 1000 ≠hPo
ùRôh¥«u TÚU A[Ü = 10.99 x 1000 ≠hPo
ùThúWô≠u APoj§ = 720 ¡/Á3
ùThúWô≠u GûP ¡úXô®p =
= 10.99 x 1000 ≠hPo x 720 ¡¡
= 720 x 10990 ¡¡
ùThúWô≠u GûP Pu²p (ùUh¬d AXÏ)
(Metric Units)
= 7912.8 Pu]v
8 úThP¬ B£h¥u APoj§ Gi 1.3 CÕEÚû[ Y¥YUô] ùRôh¥«p¨WlTlTÓ¡\Õ. CRu APoj§ûVLiÓ©¥.
Ri½¬u APoj§ = 1000 ¡/ùNÁ3
APoj§ Gi (A) JlTPoj§
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.8.26
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ClùTôÝÕ úThP¬ B£h¥u APoj§
= APoj§ Gi x Ri½¬u APoj§
= 1.3 x 1000 ¡/ùNÁ3
= 1300 ¡/ùNÁ3
§iUlùTôÚ°u APoj§ GiûQLôÔRp
§iU ùTôÚhL°u APoj§ GiLû[ ̧ rLiPYôß LôQXôm.
1 Bod¡ª¼v RjÕYm (Archemedies principle)
2 ¿oU Uô²Ls (Hydrometer)
Bod¡ª¼v RjÕYm
JÚ ¿oUj§às JÚ ùTôÚs ØtßúUô (A)TϧúVô êr¡«ÚdÏm úTôÕ AR]ôp CPmùTVodLlThP ¿oUj§u GûP AlùTôÚs¿oUj§p CZkR GûPdÏf NUUôL CÚdÏm.
¿oUj§p ùTôÚ°u GûP =
= ùTôÚ°u ùUôjR GûP - ùTôÚ°]ôp ùY°úVt\lThP ¿¬u GûP
CRu A[Ü é_ó_õVUôL CÚl©u ùTôÚs¿¬p ªRdÏm. CÕ JÚ G§o ®û]VôÏm JÚùTôÚs êr¡ CÚkRôp ARtÏ Ht\ôt úTôp¿Úm ùY°úV± CÚdÏm. AkR ¿oAlùTôÚ°u GûPVôÏm. ùTôÚs ¿¬pêr¡]ôp., AÕ úSo ®û]VôÏm.
¿¬p AªZdá¥VÕm, LûWVdá¥VÕUô]§iUj§u APoj§ Gi
§PlùTôÚû[ úRôóÜ ùNnÙmùTôÝÕ, Ri½ôó Utßm ¿ôóUj§pLûWVôR ùTôÚ[ôL CÚdL úYiÓm.CqYôß úRô óÜ ùNnVlThP§PlùTôÚ°u APôój§ GiLôQXôm.
ERôWQm
1 Lôt±p G@Ï Õi¥u GûP 160kgf UtßmØÝûUVôL Ri½ôõu êr¡CÚdÏmùTôÝÕ ARu GûP 133kgf. AkRG@Ï Õi¥u TÚU A[Ü Utßm APôój§Gi LôiL.
Lôt±p §PlùTôÚ°u GûP= 160 kgf
Ri½ôõp §Pl ùTôÚ°u GûP = 133 kgf
Ri½ôõp CZdÏm GûP = 27 kgf
Bôód¡ª¼v RjÕYj§u T¥ §PlùTôÚsRi½ôõp CZdÏm GûP = ùY°úVt \lTÓmRi½ôõu L] A[Ü
ùY°úV±V Ri½ôõp L] A[Ü= 27 cm3
§PlùTôÚ°u L] A[Ü = 27 cm3
ùTôÚ°u ̈ û\
AúR TÚUàs[ 40C p Es[ ¿¬u ̈ û\
Lôt±p ùTôÚ°u GûP
¿oUj§p CZdÏm GûP=
¿¬p AªZd á¥VÕm, LûWVd á¥VÕUô]§iUj§u APoj§ Gi
Lôt±p ùTôÚ°u GûP x ¿oUj§uAPoj§ Gi
¿¬p CZdÏm GûP=
¿ôóUj§u APôój§ Gi
§iUm ¿¬p CZdÏm GûP
AúR ùTôÚs ¿oUj§p CZdÏm GûP=
G@¡u ̈ û\Õi¥u L] A[Ü
G@Ïj Õi¥uAPoj§ =
= = 5.93
G@¡u APoj§Ri½¬u APoj§
APoj§ Gi =
G@Ï Õi¥u APoj§ Gi = 5.93
2 Lôt±p JÚ EúXôLj Õi¥u GûP 6.5 kgfUtßm Ri½ôõp 3.5 kgf AÕ ØÝûUVô]¿ôõu êr¡ CÚd¡u\Õ. ARàûPVGûPûV LôiL. ARàûPV ¿ôóUj§uAPôój§ Gi 0.8.
Lôt±p EúXôLjÕi¥u GûP= 6.5 kgf
Ri½ôõp EúXôLj Õi¥u GûP= 3.5 kgf
¿ôõp CZdÏm GûP = 3.00 kgf (6.5 - 3.5)
EúXôLj§u APôój§ Gi
Lôt±p EúXôLj§u GûP
Ri½¬p EúXôLj§u GûP=
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Bôód¡Á¼v RjÕYjûR TVuTÓj§úUtá±V Ø¥Ü A±VlTÓ¡\Õ.
¿ôóU Uô²Lû[ TVuTÓj§ ¿ôóUj§uAPôój§ GiLû[ LôQXôm. C§pùTôÕYô] ¿oU Uô² ¨dLpNu ¿oUUô²BÏm. CÕ ®j§VôNlTÓm GûP Es[B]ôp ¨ûXVô] êrÏm YûL BÏm.
¿ôóUj§u APôój§ Gi =
¿ôóU Uô²«u GûP+êrÏYRtÏ úRûYVô]GûP
¿oU Uô²«u GûP + ¿oU Uô²ûVêrL¥dLj úRûYVô] GûP (¿¬p AúRA[Ü Ï±ÂÓ YûW êr¡Ùs[ EVWm)
¿oU Uô²«u ¿oUjûR ϱdÏm ̈ ûXVô]ϱÂÓ
úUtϱl©hÓs[ A[Ü YûW«p Ri½o
¿ôóUj§p EúXôLjÕi¥u GûP= W G]dùLôsL
∴
¿ôóóUj§p EúXôLm CZdÏm GûP = 6.5kgf_W
w = 6.5 kgf - 3 kgf X 0.8 = 4.1 kgf
¿ôóUj§p EúXôLm CZkR GûP = 4.1 kgf.
3 Lôt±p §P ùUÝ¡u GûP 21 kgf. GûP 19kgf EúXôLj ÕiûPÙm ùUÝûLÙmCûQjÕ Ri½ôõp êrLûYjRôpARàûPV GûP 17 kgf BÏm. ùUÝ¡uAPôój§ Gi LiÓ©¥dLÜm.
Lôt±p ùUÝ¡u GûP = 21 kgf
EúXôLm + ùUÝ¡u, Ri½ôõp GûP= 17kgf
Lôt±p EúXôL Õi¥u GûP= 19 kgf
Ri½ôõp ùUÝ¡u GûP = 17 kgf -19 kgf
= - 2 kgf
¿¬p ùUÝ¡u GûP CZl×
= 21 kgf - (-2kgf)
= 23 kgf
Y. EúXôLm APôój§Gi ¡Wôm/L.ùNÁ
1 AÛª²Vm 2.7
2 Yôôól©Úm× 6.8 - 7.8
3 ùNm× 8.92
4 ReLm 19.32
5 CÚm× 7.86
6 DVm 11.34
7 ¨dLp 8.912
8 ùYs° 10.5
9 G@Ï 7.75 - 8.05
10 ùYsÇVm 7.31
11 ÕjRSôLm 7.14
12 ûYWm 3.51
13 ©vUj 9.78
14 ©jRû[ 8.47
15 TôvTWv ùYiLXm 8.7 - 8.9
16 Iv 0.93
17 Lôtß 0.0013
18 TôRWNm 13.56
19 ùThúWôp 0.71
20 ¼Np 0.83
21 UiùQiùQn 0.78 - 0.81
22 Ri½ôó 1.0
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.8.26
=
¿oUj§u APoj§ Gi =¿oUj§p CZkR GûP
Ri½¬p CZkR GûP
ùUÝ¡u APoj§ Gi
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78
§\]ônÜ T«t£ (Assignment)
1 ¿[m(l) = 1800 ª.Á
ALXm(b) = 65 ª.Á
EVWm(h) = 12 ª.Á
APoj§ (ρ) = 7.85¡/ùNÁ3
(m) = ________¡¡
2 ù L ô s [ Ü = 3 6≠hPo®hPm(d) = 32 ùNÁ
EVWm(H) = ___ùNÁ
3 ùY°®hPm(D) =74 ª.ÁEs®hPm(d) = 68ª.Á¿[m(l) = 115 ª.ÁAPoj§ (ρ)= 8.6 ¡/ùNÁ3
(m) = ________¡¡
4 ®hPm1(D 1 )= 80
ª.Á®hPm
2(D2)=61 ª.Á
Es®hPm(d) = 39ª.Á¿[m(L) = 112 ª.Á¿[m(l) = 90 ª.ÁAPoj§(ρ) = 7.85¡/ùNÁ3
(m) = ________¡¡
5 ®hPm(D) = 44 ª.Á®hPm(d) = 20 ª.Á¿[m(L) = 120 ª.Á¿[m(l 1) = 60 ª.Á¿[m(l 2) = 40 ª.ÁAPoj§(ρ) = 7.85¡/ùNÁ3
(m) = ________¡¡
6 ¿[m(L) = 120 ª.ÁALXm(B) = 90 ª.ÁALXm(b 1)= 60 ª.ÁALXm(b 2)= 30 ª.Á®hPm(d) = 55 ª.ÁEVWm(H) = 42 ª.ÁEVWm(h) = 18 ª.ÁAPoj§(ρ) = 7.85¡/ùNÁ3
(m) = ________¡¡
7 ¿[m(L) = 200 ª.Á¿[m
1(l 1) = 75 ª.Á
¿[m2(l 2)= 50 ª.Á
ALXm(B) = 80 ª.ÁEVWm(H) = 110 ª.ÁEVWm(h) = 45 ª.ÁAPoj§(ρ) = 2.7 ¡/ùNÁ3
(m) = ________¡¡
8 L] A[Ü(V) = 320L.ùN.ÁAPoj§(ρ) = 8.9 ¡/ùNÁ×®Dol× (g) =9.80665 ÁhPo/®]ô¥2
(m) = ________¡¡(FG)=______¨ëhPu
9 ùLôs[[Ü = 35≠hPo×®Dol×(¡) = 10ÁhPo/®]ô¥2
FG = ___ ¨ëhPu
10 ùN«²u ̈ û\(m 1 )= 150 ¡úXô
ùUôjRm FG = 8¡.¨ëhPuTÞ = ______¨ëhPu¨û\ (m2)= __¡úXô
11 GûP(W) (FG) = 22.5¨ëhPu
L] A[Ü (volume) =______
12 ®ûN(F) = 250 d N
L] NÕWj§uTdLm = ______ ª.Á
(L] NÕWj§uùY«h úTXuv`F')
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13 Au TôXuÑÓúXôh ùNh Al=16 cNú T X u £ eGûP«u ®hPm ø= 20 ª.Áú T X u £ eGûP«u A[Ü (l)=______ ª.Á
14 ®hPm(d 1)= 40 ª.Á
¨û\(m 1)= 9 x 10 –2
¡¡
BWm 1 = BWm 2
®hPm(d 2)= 60 ª.Á
FG 2 = ______¨ëhPu
15 ¿[m(l) x ALXm(b)= 1 Á2
FG = 7.85 x 10–2
¡.¨ëhPuL]m(s) = ______ ª.Á
16 ®ûN (F) = 400¨ëhPu
(m) = ________¡¡
17 ¨û\1(m 1)= 200
¡Wôm
FG = 16 ¨ëhPu
®ûN(F) = ______ dN
18 R = 14 ¡. ¨ëhPu
(m) = ________¡¡
19 L] A[Ü(V) = 4ùP.Á3
FG = 10.8 daN
APoj§(ρ) =______¡/ùNÁ3
20 ¿[m(l) = 500 ª.ÁALXm(b) = 300 ª.ÁEVWm(H) = 250 ª.ÁG i ù Q n « uAPoj§(ρ) = 0.9¡/L.ùNÁ3
¨û\(m) = 2.5 kgEVWm(h) = ____ª.Á
21 G g £ u á ≠ eúPhPô ùLôÓdLlT h Ó s [ Õ .ú R ¥ ú V h P ¬ pRi½o = 10≠hPoLiÓ©¥Ri½¬u ¨û\ =__________ ¡¡(JÚ ≠hPo = ùP£ÁhPo3 L]A[Ü)Ri½¬u APoj§= 1 ¡¡/ùP..Á3
22 EÚû[«u ¿hPpA[ÜLsùLôÓdLlThPúPhPôù Y ° l × \®hPm(OD) = 111ª.Á
Eh×\ ®hPm(ID) = 103 ª.Á¿[m = 240 ª.ÁùTôÚs = C.I = Yôol× CÚm×Yôol©Úm©u APoj§ (C.I) = 7.259 ¡/ùNÁ3
CRàûPV ¨û\ûVd LiÓ©¥ _________ ¡¡
23 LhCVôu ©u(§PUô]Õ)ùLôÓdLlThPúPhPô®hPm = 200 ª.Á¿[m = 70 ª.ÁùTôÚs = (M.S)ªÚÕ G@ÏAPoj§ = 7.85 ¡/ùNÁ3
CRàûPV¨û\ûVLiÓ©¥dLXôm¨û\ ________ ¡
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24 A Û ª ² V m©vPuù L ô Ó d L l T hÓs[Õ úPhPô®hPm = 80 ª.Á¿[m = 100 ª.ÁA Û ª ² V j § uAPoj§ = 2.7 ¡/ùNÁ3
CRàûPV ¨û\_______ ¡¡
25 EsÇPt\ EÚû[(Lôvh ©Wôv)ùLôÓdLlThPúPhPôùY°l×\®hPm(O.D) = 150 ª.ÁEh×\®hPm(I.D) =120 ª.Á
©jRû[«u APoj§ = 6.89 ¡Wôm/L] ùNÁ
ãj§WjûR TVuTÓjRp = ( (R3)3)
LiÓ©¥dLÜmEsÇPt\ EÚû[«u ¨û\ = _______ ¡¡
26 ¼Np ùRôh¥
ùLôÓdLlThPúPhPô
®hPm = 400 ª.Á
¨Wl×m BZm (h)= 600 ª.Á
vTôu_õ B@l B«p = 0.8
Ri½¬u APoj§ = 1000 ¡¡/Á3
LiÓ©¥
ùRôh¥«p Es[ B«≠u ¨û\ = ______ ¡¡
27 YûWVßdLÜm
¸rLiP ùNôtLû[ YûWVßdLÜm
a ¨û\
b GûP
c APoj§
d APoj§ Gi
28 Yi¥«u GûPûV Uôt\m ùNnVÜm
×®Dol× (g) = 10 Á/®]ô¥2
®ûN GûP ¨û\
a 480 ¨ëhPu _______
b 14800 ̈ ëhPu _______
c 2000 ¨ëhPu _______
d 7000 ¨ëhPu _______
29 Yi¥«u ¨û\ AXûL Uôt± GÝRÜm
×®Dol× (g) = 9.81 ÁhPo/®]ô¥2
Yi¥«u ¨û\ ARu GûP«p
a 1200 ¡¡ ________ ̈ ëhPu
b 800 ¡¡ ________ ̈ ëhPu
c 700 ¡¡ ________ ̈ ëhPu
d 900 ¡¡ ________ ̈ ëhPu
30 úLô¥hP CPeLû[ éoj§ ùNn
EúXôLjûRÙm §WYjûRÙm Jl©PÜm
ùTôÚhLs APoj§ APoj§ Gi
a DVm 11.34 _______
b ùNm× 8.92 _______
c Yôol× CÚm× 7.20 _______
d ùThúWôp 0.71 _______
e ¼Np 0.83 _______
f Npé¬d B£h 1.84 _______
31 a Utßm b «p úLô¥hP CPeLû[ N¬Vô]YôojûRL[ôp ¨WlTÜm.
a Ri½¬u APoj§ = 1000 ¡¡/ÁhPo3.
ûSh¥¬d B£h¥u APoj§ Gi 1.2Gu\ôp ûSh¥¬d B£h¥u APoj§ =_______
b ùTôÚhLs APoj§ APoj§ Gi
i Ri½o 1000 ¡¡/Á3 _______
ii AÛª²Vm 2.7 ¡/ùNÁ3 _______
iii CÚm× 8 ¡/ùNÁ3 _______
iv ùNm× 8.7 ¡/ùNÁ3 _______
c ùTôÚ°u ¨û\ = L]A[Ü x _______
d ®ûN«u GûP = ¨û\ x _______
e CRu ÑÚdLeLû[ GÝÕL
i ùULô¨ëhPu_______
ii ¡úXô¨ëhPu To vùLôVo ÁhPo_______
f JÚ ≠hPo Ri½o _______¡¡.
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KnÜ, CVdLm, úYLm, §ûN úYLm, úYLm Utßm §ûNúYLj§tLô]úYßTôÓ, ØÓdLm Utßm Ïû\ØÓdLm T«t£ 1.9.27
ùTôÚ°u KnÜ ¨ûX (Body at rest)
JÚ ùTôÚs Ñtß×\ ãr¨ûXdÏ HtT Ru¨ûX«p CÚkÕ Uô\ôUp CÚlTÕ KnܨûX G]lTÓm.
ùTôÚ°u CVdLm (Body at motion)
JÚ ùTôÚs Ko CPj§≠ÚkÕ úYßJÚCPj§tÏ Ru ̈ ûXûV Uôt±d ùLôsYRtÏARôYÕ CP Uôt\m AûPYRtÏ CVdLmGuß ùTVo. JÚ ùTôÚs CVeÏmúTôÕúSodúLôh¥p CPm ùTVokÕ ùNpÛUô«uAq®VdLm úSodúLôhÓ CVdLm G]lTÓm.JÚ ùTôÚs CVeÏm TôûR Yû[YôLAûUÙUô]ôp Aq®VdLm YhP Nôôó×CVdLm G]lTÓm.
CVdLm NmTkRlThP ùNôtLs (Termsrelating to motion)
CPlT«t£ (Displacement)
ùTôÚ°u ùRôPdL ¨ûXdÏm, Cߧ¨ûXdÏm CûPúV úSôódúLôh¥p Es[çWm AlùTôÚ°u CPlùTVof£G]lTÓm.
úYLm (Speed)
JÚ CVeÏm ùTôÚs JÚ Ï±l©hP úSWj§pSLÚm çWm úYLm G]lTÓm. CRtÏ A[ÜUhÓúU EiÓ. §ûN¡ûPVôÕ. G]úY CÕvúLXôo A[YôÏm.
úYLm= JÚ Ï±l©hP AXÏ úSWj§p SLÚmçWm.
AXÏ = ÁhPo/ùNLih, ¡úXôÁhPo/aYo(U¦)
§ûN úYLm (Velocity)JÚ CVeÏm ùTôÚs JÚ Ï±l©hP úSWj§pϱl©hP §ûN«p ùTßm CPlùTVof£úVAlùTôÚ°u §ûN úYLm G]lTÓm. CûRϱl©ÓmùTôÝÕ Gi U§lûTÙm§ûNûVÙm úSodúLôh¥p ϱl©PúYiÓm. G]úY CÕ ùYdPôôó A[YôÏm.§ûN úYLm úSodúLôh¥úXô ApXÕúLôQ §ûN«úXô CÚdLXôm úSodúLôh¥p CVeÏm §ûN úYLj§u AXÏÁhPo/ùNLih,
¡úXôÁhPo/U¦, ûUp/U¦
úYLm Utßm §ûN úYLj§u úYßTôÓLs
úYLm §ûNúYLm
úYLm GuTÕ JÚ §ûNúYLm GuTÕ JÚùTôÚs JÚ ùTôÚs JÚ Ï±l©hP®]ô¥ úSWj§p §ûN«p JÚ ®]ô¥SLÚm çWm BÏm úSWj§p ùTßm CPl
ùTVof£ BÏm.
úYLj§p §ûN §ûN úYLj§p ARuϱl©ÓYÕ Gi U§l×, §ûN B¡VCpûX úYLm CWiÓm ϱdLlTÓmARu Gi U§l©p UhÓúUϱdLlTÓm
úYLm = §ûNúYLm =(LPkR çWm)
GÓjÕdùLôiPçWm
=ϱl©hP §ûN«p
CPlùTVof£
GÓjÕdùLôiPúSWm
=
ØÓdLm (Acceleration)
JÚ ùTôÚ°u §ûN úYLm UôßmúTôÕAlùTôÚs ØÓdLm ùTß¡\Õ. JÚùTôÚ°u ØÓdLm GuTÕ JÚ Ï±l©hPúSWj§p §ûN úYLj§p HtTÓmUôßTôPôÏm. CRu AXÏ ÁhPo/ùNLih2.CÕ JÚ ùYdPôôó A[YôÏm.
ØÓdLm (a) =
AXÏ = ÁhPo/ùNLih2
u = BWmT §ûNúYLm (Á/ùNLih)
v = Cߧ §ûNúYLm (Á/ùNLih)
s = CûPlùTVof£ (ÁhP¬p)
t = LôXm (A) úSWm (®]ô¥)
a = ØÓdLm (Á/ùNLih2 (úSoUû\«p)
R = G§oØÓdLm (A) úYLjR[of£ (Á/ùNLih2 (G§oUû\«p)
CVdL NUuTôÓLs (Equations of motion)©\Ï v = u + at
ùTôÚ°u Cߧ §ûN úYLm =BWmT§ûNúYLm + ØÓdLm x LôXm
s = ut + at2 Utßm v2 – u2 = 2as
v2 = u2 + 2as
LPkR çWm
GÓjÕdùLôiPçWm=
§ûNúYLj§p HtTÓm UôßRp
LôXmÁ/ùN2
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G§o ØÓdLm (A) úYLjR[of£ (Retardation)
JÚ ùTôÚ°u Cߧ §ûN úYLjûRLôh¥Ûm BWmT §ûN úYLm Ïû\YôLCÚkRôp. ARtÏ ØÓdLm Guß ùTVo. JÚùTôÚ°u BWmT §ûN úYLjûR Lôh¥ÛmCߧ §ûN úYLm Ïû\YôL CÚkRôp ARtÏG§oØÓdLm G]l ùTVo. êuß CVdLNUuTôÓLs Es[].
v = u – at
Cߧ §ûN úYLm=BWmT§ûNúYLmþØÓdLm x úSWm
s = ut – at2
CPlùTVof£ = BWmT§ûN úYLmxúSWmþØÓdLmxúSWm2
u2–v2 = 2as
BWmT§ûN úYLm2þCߧ §ûN úYLm2 = 2 xØÓdLm x CPlùTVof£
NWôN¬ úYLm (Average speed)
Vm - NWôN¬ úYLm ÁhPo/¨ªPm, (ÁhPo/ùNLih)
n - YhP CVdLm JÚ ¨ªPj§tÏ ApXÕJÚ ¨ªPj§p GjRû] vhúWôd
s - CPlùTVof£, vhúWôd¡u ¿[m
ÅfÑ úYLm (Stroke speed) (TPm 1)
¡Wôe©u kþ×s°«p JÚ Ñtß Ñt±]ôp,AkR çWj§tÏ TYoNô ©ú[h SLÚm çWm= 2 x s
BûLVôp JÚ ¨ªPj§tÏ ‘n’ Ñtß çWmÑt±]ôp ARu çWm = 2 x s x n. ©ú[¥uÅfÑ ÁhP¬p ùLôÓdLlTÓYR]ôp NWôN¬úYLjûR LôQ
Vm = 2 x s x n
©vPu úYLm (Piston speed) (TPm 2)
©vPu Øuàm ©uàm SLÚm úUpTϧUtßm ¸r Tϧ«p Es[ ùPhùNuP¬pARu úYLm JúW ºWôL Uô± ùLôiúPCÚdÏm. CkR úL£ÛmáP NWôN¬ úYLm
Vm = 2 x s x n -I ªp≠ ÁhP¬Ûm Utßm n IJÚ ¨ªPj§tÏ GjRû] ÑtßdLs GußmUtßm Vm I ÁhPo /ùNLih¥pá\lThÓs[Rôp.
Vm = 2 x s x ÁhPo/¨ªPm
=
S I ÁhP¬p ùLôÓjRôp ©\Ï
Vm = 2 x s x = s x ÁhPo/ùNLih
2 x s CWiÓ ÅfûN ϱdÏm.¬£l×úWôd`u CVdLj§p, NWôN¬úYLjûR LQd¡p GÓjÕdùLôs[úYiÓmVm = 2 x s x n ÁhPo/¨ªPm C§p s IÁhP¬p ùLôÓdLlThÓ CÚkRôp.
ERôWQm (Example) (TPm 3)
GdvhÚNu ©Wv£p Es[ ¡Wôe¡u BWm20 ùN.Á Utßm ARu úYLm 30 rpm NWôNôõúYLjûR ÁhPo /¨ªPm, ÁhPo/ùNLih¥pLQd¸Ó ùNnVÜm.
s = ®hPm = 40 ùNÁ
¡Wôe JÚ Øû\ Ñt±]ôp ©vPu SLÚmÕWWm 2s = 80 ùNÁ
Vm = 2 x 400 x ÁhPo/¨ªPm
= 24 ÁhPo/¨ªPm = 0.4 ÁhPo/ùNLih
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.9.27
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83
¨ëhP²u CVdL ®§Ls (Newton laws ofmotion)
×®Dol× ®ûNVôp HtTÓm CVdLj§uNUuTôÓ (Equations of motions under gravity)
úUp úSôd¡ ¸r úSôd¡
V = u – gt v = u + gt
s = ut – gt2 s = ut + gt2
u2–v2 = 2as V2–u2 = 2as
×®Dol× ®ûNVôp HtTÓm CVdLm (Motionunder gravity)
JÚ ùTôÚs ¨ûX«p CÚkÕ ¸r úSôd¡®ÝmúTôÕ ARàûPV §ûN úYLmA§L¬dÏm Utßm RûWûV ùRôÓmùTôÝÕARu §ûN úYLm A§L ThNUôL CÚdÏm.BûLVôp ×®Dol× ®ûNVôp JÚ ùTôÚs¸rúSôd¡ YÚmùTôÝÕ ºWô] ØÓdLmHtTÓ¡\Õ. CkR CVdLm úUpúSôd¡CVeÏmùTôÝÕ, AkR ùTôÚÞdÏG§oØÓdLm HtTÓ¡\Õ CkR ØÓdLm×®DolTôp HtTÓ¡\Õ. CÕ ‘g’ GußϱdLlTÓ¡\Õ.
EkRm (Momentum)
JÚ CVeÏm ùTôÚs Utù\ôÚ ùTôÚÞPuúUôÕmúTôÕ, A§p AûNûY EiPôdÏm§\ûU EkRm G]lTÓm. CÕ ¨û\ûVÙm§ûN úYLjûRÙm ùTÚd¡ YÚm ùRôûLdÏNUm BÏm. EkRj§u AXÏ ¡úXô ÁhPo/ùNLih.
EkRm = ùTôÚ°u ¨û\ x §ûN úYLm
¨ëhP²u CVdL ®§Ls (Newton’s laws)
ØRp ®§ (First law)
RuÁÕ ùY°®ûN HÕm RôdLôRYûWJqùYôÚ ùTôÚÞm R]Õ AûNVô¨ûX«úXô ApXÕ ºWô] §ûN úYL¨ûX«úXô ùRôPokÕ CÚdÏm.
CWiPôm ®§ (Second law)
JÚ ùTôÚ°u EkRm Uôßm ÅRm ARuúUp ùNVpTÓm ®ûNdÏ úSo®¡Rj§pAûUYúRôÓ Aq®ûN«u §ûN«úXúVCÚdÏm.
êu\ôm ®§ (Third law)
JqùYôÚ ®ûNdÏm ARtÏ NUUô]G§o®ûN Juß EiÓ.
¬®h CûQl©p v¥Wôl ÁÕ NUUô] ®ûNùNVpTÓ¡\Õ Utßm AÕ G§o §ûN«ÛmùNVpTÓ¡\Õ. F2. (TPm 4)
EkR A¯®uûU ®§ (Law of conservation ofmomentum)
JußdÏ úUtThP ùTôÚsLsúUô§dùLôsÞmúTôÕ úUôRÛdÏ ØuEs[ ùUôjR EkRlTôÓ úUôRÛdÏl©uEs[ ùUôjR EkRlTôh¥tÏfNUm ApXÕúUôRÛdÏ ©\Ï HtTÓm EkRm éw´VmBÏm.
m1 - JÚ ùTôÚ°u ¨û\
v1 - SLÚmùTôÝÕ HtTÓm §ûN úYLm
m2 - CWiPôYÕ ùTôÚ°u ̈ û\
v2 - SLÚmùTôÝÕ HtTÓm §ûN úYLm
EkRm = ¨û\ x §ûNúYLm = ùTôÚ°u ¨û\x ARu §ûNúYLm
EkR®¡R Uôt\m = ùTôÚ°u ÁÕ HtTÓm®ûN
( )F
t
uVm =
−⎟⎠⎞
⎜⎝⎛
®ûN = ¨û\ x ØÓdLm
CmTôdhÓdÏ Øu]ôp CWiÓ ùTôÚ°uEkRm = CmTôdhÓdÏ ©\Ï HtTÓm EkRm.
m1 x v1 + m2 x v2 = (m1 + m2)V
LûX ùNôtLs - YôL]eL°p Es[ £XERôWQeLs (Terms - Some Examples in vehicles)
CPlùTVof£ (Displacement)
©vP²u CPlùTVof£ GuTÕ CWiÓùPh ùNuPÚdÏ CûPúV Es[CûPùY° (TDC Utßm BDC) £≠iP¬p©vPu SLÚm çWm. (TPm 5)
úYLm (Speed)
CûR CWiÓ YûL«p ϱl©PlTÓ¡u\Õ.
– YôL]j§u úYLm - in kmh/mph
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– CVk§Wj§u úYLm - in rpm
§ûN úYLm (Velocity)
JÚ úUôhPôó YôL]m, ùTôÕYôL TôûR«pùNpÛm ùTôÝÕ ARàûPV úYLm Utßm§ûN«p UôßRp HtTÓm. AR]ôp CûRdùLôiÓ YôL]j§u §ûN úYLmLQd¡PlTÓ¡\Õ.
ØÓdLm (Acceleration) (TPm 6)
TôûR«p YôLj§u úYLm A§L¬dÏmùTôÝÕ CÕ ØÓdLm G]lTÓ¡\Õ.
Ïû\ØÓdLm (A) G§o ØÓdLm (CÕ úUÛm® [ d L l T h Ó s [ Õ ) Y ô L ] mùNpÛmùTôÝÕ, ©úWd úTôhPôp,YôL]j§u úYLm Ïû\¡u\Õ. CÕÏû\ØÓdLm ApXÕ G§oØÓdLmG]lTÓ¡\Õ.
YhP ApXÕ úLôQ CVdLm (Circular orAngular motion) (TPm 7)
JÚ ùTôÚs AfûN ûYjÕ ÑZÛmùTôÝÕARu CVdLjûR úLôQ CVdLm (A) YhPCVdLm Guß ùNôp¡ú\ôm.
ERôWQm
JÚ ùTôÚs YhP TôûR«p CVeÏmùTôÝÕ (`ôlh, AfÑLs, ¡VoþÅpLs,
Ll©Ls (pulleys), ©û[ ÅpLs, ¡ûWi¥eÅpLs) B¡VûYLs JÚ ̈ ûXVô] úYLj§pAfûN Ñt± CVeÏ¡u\].
YhPúLôQ CVdLjûR úLôQj§ûN úYLmGußm ApXÕ ùT¬l©Wp úYLm GußmAûZd¡ú\ôm.
CRu AXÏ ÁhPo /ùNLih(A) úW¥Vu/ùNLih BÏm.
ùTôÚhLs KnÜ ¨ûX Utßm CVdL¨ûX (Bodies at rest and in motion)
©úWd £vPj§p ùRôPo×ûPV LûXfùNôtLs (Terms related to brake system)
JqùYôÚ YôL]j§tÏm R²VôL ©úWdAûUl× Es[Õ. CVeÏm YôL]j§tÏ©úWd úTôhPôp (ϱl©hP §ûNúYLjÕPu ) CRàûPV §ûN úYLmÏû\¡u\Õ Utßm YôL]j§tÏ G§oØÓdLm HtTÓ¡u\Õ Utßm £±Õ çWmùNu\ÜPu YôL]m ̈ u߮ӡu\Õ. G]úY©úWd úTôÓYRtÏ LûXfùNôp≠u ®[dLm¸úZ Lôi©dLlThÓs[Õ.
G§o ØÓdLm (Deceleration) (a) (TPm 8)
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JÚ Ï±l©hP úSWj§p §ûNúYLmÏû\dLlTÓYÕ. ERôWQm
JÚ Lôôó U¦dÏ 90 ¡úXô ÁhPo úYLj§pùNp¡\Õ AûR 10 ùSô¥L°p¨ßjRlTÓ¡\Õ.
G§oØÓdLm = 90 x x 1/10
= 25 ÁhPo/ùNLih/10 ùNLih
= 2.5 ÁhPo/ùNLih2
G§o ØÓdLj§u úSWm (Deceleration time)
10 ùSô¥ GuTÕ LôûW ̈ ßjÕYRtLô] úUúXϱl©hP úSWUôÏm.
¨ßjÕYRtLô] çWm (Stopping distance)
G§o ØÓdLj§uúTôÕ, Lôo SLokR çWmARôYÕ ̈ tTRtLôL GÓjÕdùLôiP çWm‘d’ G] AûZdLlTÓ¡\Õ.
Cߧ«p ¨tÏm ùUôjR çWm GuTÕ.NôRôWQUôL ̈ tLdá¥V çWm Utßm Yi¥KhÓTY¬u ùNnúYLj§tÏs Lôo SLÚmçWm B¡VûYLs ùLôiPÕ.
¬Vôd`u ûPm ¸úZ ®Y¬dLlThÓs[Õ.
©úWdûL úTôÓmùTôÝÕ, JhÓSo£XúSWeL°p BTj§u RuûUûV EQokÕ©\Ï ©úWdûL úTôÓ¡\ôo. CkR LôXCûPùY°Rôu ¬Vôd`u úSWm G]lTÓm.YôL]m ¨tTRtÏ Øu, YôL]m CVeÏm£±Õ çWm Utßm JhÓSo ùNVpTPGÓjÕdùLôs[lTÓm úSWm Cߧ«p¨tÏm ùUôjR çWm YôL] Kh¥L°u¬Vôd`u úSWjûR ùTôÚjÕ UôßTÓm.¬Vôd`u úSWm JhÓSÚdÏ JhÓSoúYßTÓm.
ERôWQm
JÚ Lôôó JÚ U¦dÏ 72 ¡úXô ÁhPôó úYLj§pCVeÏ¡\Õ. ARàûPV ØÓdLm (a) 5ÁhPôó/ùNLih2 Yi¥ KhÓTYôõu ôõVôd`uúSWm 1.5 ùSô¥Ls. GqY[Ü çWj§p Yi¥¨tÏm GuTûR LQd¡Ó ùNnL.
¾ôóÜ
Lôôõu §ûN úYLm = 72 kmph
= 20 Á/ùNLih
ØÓdLm = 5 Á/ùNLih2
ùTôÕYô] ¨tÏm çWm
S = (ÁhPô)
¨tÏm GÓjÕd ùLôiP ùUôjR çWm
= 40 ÁhPôó + §ûNúYLm x ôõVôd`u çWm
= 40 Á + (20 x 1.5) Á
= 70 ÁhPoLs
¨ëhP²u CVdL ®§Ls (Newon's Law ofMotion)
YôL]eL°p Es[ £X ERôWQeLs
ØRp ®§ (ERôWQjÕPu) First law (withexamples) (TPm 9)
ùTôÚsLs KnÜ ¨ûX«p (A) ºWô]CVdLj§p (Bodies at rest or in Uniform motion)
TDC (A) BDC NPjÕYj§p CÚdÏmùTôÝÕ¼Np CVk§Wj§u ©vPu KnܨûX«úXVúV CÚdÏm. úLv AÝjRm®ôõ®ûPÙmùTôÝÕ (A) TDC ApXÕ BDC«p CÚkÕ, ©û[ Å≠u úYLj§¦Ü êXm©vPu CVeÏ¡\Õ.
CWiPôm ®§ (ERôWQjÕPu) (Secondlaw (with examples) (TPm 10)
JÚ ùTôÚ°u EkRm Uôßm ÅRm ARuúUp ùNVpTÓm ®ûNdÏ úSôó ®¡Rj§pAûUYúRôÓ Aq®ûN«u §ûN«úXúVCÚdÏm.
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– CVdLj§p Es[ Lù]d¥e Wôh BDC«pKnÜ ¨ûXdÏ YÚ¡u\Õ.
– Lôt±u ®ûN«u ÅfÑ LôWQUôLYôL]j§u CVdL §ûN UôßTôÓAûP¡\Õ.
– YôL]m ¸r úSôd¡ NôõYô] TôûR«pùNpÛm ùTôÝÕ ARu úYLmA§Lôõd¡\Õ.
– YôL]m úUp úSôd¡ NôõYô] TôûR«pùNpÛm ùTôÝÕ ARu úYLm Ïû\¡\Õ.
êu\ôm ®§ (ERôWQjÕPu) Third law (withexamples) (TPm 11&12)
JqùYôÚ ®ûNdÏm ARtÏf NUUô]G§ôó®ûN Juß EiÓ.
GpXô úUp úSôd¡V ®ûN = GpXô¸rúSôd¡V ®ûN
– §ÚÏj çd¡ ¥TWu£Vp -I çdÏ¡\Õ.
– ¡úWu L«ß Cu_öû] -I çdÏ¡\Õ.
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úYLm Utßm §ûNúYLj§tÏ ùRôPo×ûPV LQdÏLÞm §\]ônÜT«t£LÞm T«t£ 1.9.28
ERôWQeLs (Examples)
• JÚ ùTôÚs 168 ÁhPôó çWm úSôó úLôh¥p21 ùNLi¥p ùNp¡u\Õ. GqY[Ü §ûNúYLj§p ClùTôÚs ùNp¡u\Õ.
§ûNúYLm = LPkR çWm/úSWm
= 168 ÁhPôó/21 ùSô¥Ls
= 8ÁhPôó/ùSô¥
• JÚ W«p, 150 ¡.Á CûPùY° Es[ CWiÓW«p ¨ûXVeLû[ 2 1/2 U¦ úSWj§pLPkÕ ùNp¡\Õ G²p W«≠u NWôNôõ§ûN úYLjûR LôiL.
NWôNôõ §ûN úYLm = LPkR çWm/ GÓjÕdùLôiP úSWm
= 150 ¡Á/2 1/2 U¦ = 52150
25
150×=
Á/U¦
= 60 ¡Á/U¦
• JÚ YôL]m, ºWô] ØÓdLjÕPu, ARu§ûN úYLm 8 ¡Á/U¦ ≠ÚkÕ 24 ¡Á/U¦þI. 4 ùLNihþp AûP¡u\Õ G²pARu ØÓdLjûR LiÓ©¥ UtßmùNLih¥p YôL]m LPkR çWjûRÙmLiÓ©¥.
BWmT §ûN úYLm (u) = 8 ¡Á/U¦ (u)
Cߧ §ûN úYLm (v) = 24 ¡Á/U¦ (v)
GÓjÕdùLôiP úSWm (t) = 4 ùNLih (t)
∴ v = u + at
24 ¡Á/U¦ = 8 ¡Á/U¦ + a x 4 ùNLih
(24 ¡Á/U¦ - 8 ¡Á/U¦ - 16 ¡Á/U¦)
∴ 4a ùNLih = 16 ¡Á/U¦ = 16000 ÁhPôó/3600ùNLih
∴ ØÓdLm (a) = 16000 ÁhPôó/3600 x 4 ùNLih2
∴ ØÓdLm = 1.1 ÁhPo/ùNLih2
∴ LPkR çWm 4a = 4 x 1.1 = 4.4 ÁhPo
• JÚ Lôôó 50 ¡Á/U¦ §ûN úYLj§pùNußùLôi¥Úd¡\Õ. AÕ 45 ùNLi¥p¨ßjRlTÓ¡\Õ G²p ARu G§ôóØÓdLjûR LôiL.
BWmT §ûN úYLm (u) = 50 ¡Á/U¦ (1 ¡Á =1000 ÁhPov)
Cߧ §ûN úYLm (v) = 0 ¡Á/U¦ (1 U¦ =3600ùNLihv)
GÓjÕdùLôiP úSWm (t) = 45 ùNLih
v = u – at
0 = u – at
u = at
50000/3600 ÁhPôó/ùNLih = a x 45 ùNLih
∴G§o ØÓdLm = 50000/3600 x 45 ÁhPôó/ùNLih2
= 0.30 ÁhPôó/ùNLih2
• ×®Dôól× ®ûNVôp, JÚ ùTôÚs úUúXCÚkÕ ¸úZ RûW«p ®ÓYRtÏ JÚùNLih B¡u\Õ. ùTôÚs GqY[ÜEVWj§p CÚkÕ ¸úZ ®ÝkRÕ GußLôiL. g = 9.81 ÁhPôó/ùNLih2.
BWmT §ûN úYLm (u) = 0 ÁhPôó/ùNLih
×®Dôól× ®ûNVôp HtTÓm ØÓdLm = 9.81ÁhPôó/ùNLih2
GÓjÕdùLôiP úSWm (t) = 1 ùNLih
= ut + gt2 0 x 1 ùNLih = x 9.81 Á/ùNLih2
x 12 ùNLih
= 0 x 1 ùNLih c + x 9.81 Á/ùNLih2 x 1
ùNLih2
1 ùNLih2 = 4.905 ÁhPo s = 4.905 ÁhPo
• JÚ ùTôÚs AûNVôUp CÚdÏm ùTôÝÕARu ÁÕ 30 ̈ ëhPu ®ûN ùNVpTÓ¡\Õ.AlùTôÚ°u ̈ û\ 50 ¡úXô. 4 ùNLi¥tÏ©\Ï ùTôÚ°u §ûN úYLjûR LiÓ©¥Utßm LPdÏm çWjûRÙm Utßm ARuØÓdLjûRÙm LôiL.
®ûN (F) = ¨û\ (m) x ØÓdLm (a)
30 ¨ëhPu = 50 ¡úXô x a
3 ¡úXô x ÁhPôó/ùNLih2 = 50 ¡úXô x a
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∴ ØÓdLm = 3/50 ÁhPôó/ùNLih2
∴ a = 0.06 ÁhPôó/ùNLih2
v = u + at
= 0 + 0.06 ÁhPôó/ùNLih2 x 4 sec = 0.24 ÁhPôó/ùNLih
s = ut + 1/2 at2 = 0 + 1/2 x 0.06 ÁhPôó/ùNLih2 x 16ùNLih2
s = 0.48 ÁhPôó
• úUpúSôd¡ ùNeÏjRôL G±VlTÓmLp≠u §ûN úYLm 120 ÁhPôó/ùNLih (a)úU≠ÚkÕ ¸rúSôd¡ §Úm×YRtÏ ØuAÕ GhÓm A§LThN EVWm LôiL (b)úUúX ùNuß ¸r úSôd¡ YW ùUôjRmGÓjÕd ùLôiP úSWjûRd LôiL. (c)RûWûV ùRôÓm úTôÕ CRu §ûN úYLmGu] GuTûRd LôiL.
Lp≠u BWmT §ûNúYLm = 120 ÁhPôó/ùNLih
Cߧ §ûN úYLm = 0 ÁhPôó/ùNLih
×®Dôól× ®ûNVôp HtTÓm G§ôó ØÓdLm= 10 ÁhPôó/ùNLih2
u2–v2 = 2g.s
∴ 1202 ÁhPôó2/ùNLih2 – 0 = 2 x 10 ÁhPo/ùNLih2 x s
∴ s = 120 x120/2 x 10 ÁhPôó
= 720 ÁhPôó
¸r úSôd¡ YÚmúTôÕ ARàûPV BWmT§ûN úYLm = 0 ÁhPo/ùNLih Utßm×®DolTôp HtTÓm ØÓdLm = 10 ÁhPo/ùNLih2 Utßm LPkR çWm = 720 ÁhPo.
∴ v2– u2 = 2as
v2– 0 = 2 x 10 ÁhPo/ùNLih2 x 720 ÁhPo
∴ v = 120 ÁhPo/ùNLih
úUp úSôd¡ ùNpX GÓjÕdùLôiP úSWmUtßm ARu §ûNúYLm = 0 ÁhPôó/ùNLih= u/g = 120 ÁhPôó/ùNLih/10 ÁhPôó/ùNLih2
= 12 ùNLih
KnÜ ̈ ûX«p CÚkÕ §ûNúYLm 120 ÁhPôó/ùNLih AûPV GÓjÕd ùLôiP úSWm= v/g = 12 ùNLih.
∴ GÓjÕdùLôs[lThP ùUôjR úSWm.
• Gu_õu ©û[ Åp 2800 rpm þp ÑZp¡u\ÕARàûPV úLôQ§ûN úYLjûR úW¥Vu/ùNLi¥p LQd¡ÓL. (TPm 1 & 2)
úLôQ §ûN úYLm (W) = JÚ Ï±l©hPúYLj§p HtTÓm CPlùTVôóf£ (A) úLôQ§ûN«p ÑtßYÕ CRu AXÏ úSWm BÏm.
¾ôóÜ
©û[ Å≠u úLôQ A[Ü §ûN úYLm W= 2πN/60 úW¥Vu/ùNLih [N = 2800rpm]
= 2π x 2800/60 úW¥Vôu/ùNLih.
= 293.3 úW¥Vôu/ùNLih.
• JÚ úUôhPôôó Lôôó NdLWj§u ®hPm 540ª.Á. CÕ 120° úLôQj§p §Úmס\ÕG²p. PVôõu JÚ ×s° GqY[Ü çWmSLÚm.
¾ôóÜ
NdLWm JÚ Ñtß ÑtßYRtÏ JÚ 2π úW¥VuBÏm. ARôYÕ, 2π úW¥Vu = 360°
NdLWm 120° úLôQj§p ÑZp¡\Õ,
120° = 120 x 2π/360
= 2.094 úW¥Vuv
PVôõu JÚ ×s° SLôókR çWm S – re
[where r = 270 ª.Á
θ = 2.094 úW¥Vu]
S = 270 x 2.094 ªÁ
JÚ ×s° YhP TôûR«p SLôókR çWm =565.380ª.Á
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= 24 ùNLih
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• Lôôõu ©u NdLWj§u ®hPm 600 ª.Á©u×\ Bd£p 250 rpm þ p CVeÏ¡\Õ.©u×\ NdLWj§u úYLjûR ÁhPôó/ùNLi¥p LiÓ©¥.
¾ôóÜ
YhP úYLm V = ÁhPo/ùNLih
• JÚ Lôôó 72 km/h úYLj§p ùNp¡u\Õ.ARu ØÓdLm 5 ÁhPô/óùNLih2 ARu¨ßjÕm çWjûR LiÓ©¥dLÜm.
ÁhPo/ùNLih
¾ôóÜ
Va (Lôôõu BWmT úYLm) = 72 kmph
= 20 ÁhPôó/ùNLih
= 20 ÁhPo/ùNLih
¨ßjÕm çWm S = (ÁhPo)
ÁhPo
ÁhPo/ùNLih)
§\]ônÜ T«t£ (Assignment)
1 S = 180 ª.Á
n = 65 (P×svhúWôd)
Vm = _____Á/¨ªPm
(Vm GuTÕ NWôN¬ùYhÓm úYLm)
2 V = 16 Á/¨ªPm
s = 210 ¨ªPm
n = ______
3 (V GuTÕ NWôN¬ùYhÓm úYLm)
n = 22 vhúWôdv(P×s vhúWôd)/¨ªPm
V = 18 Á/¨ªPm
s = ______ ª.Á
4 s = 240 ª.Á
n = 30 (Jod¡evhúWôd)
V = ______ Á/¨ªPm
5 n = 50 Lh¥evhúWôd
V = 32 Á/¨ªPm
d = ______ ª.Á
s = 64 ª.Á
6 n = 3600 rpm
Vm = _____ÁhPo/ùNLih
Vm GuTÕ ©vP²uNWôN¬ úYLm BÏm)
7 Vm = 0.35 .ÁhPo/ùNLih
s = 200 ª.Á
n = ______ rpm
8 s = 650 ª.Á
Vm = 90 Á/¨ªPm
n = ______ rpm
9 Vm1 = 5.2 ÁhPo/ùNLih A§L¬dLlTÓ¡\Õ
Vm2= 6.3 ÁhPo/ ùNLih
A§L¬dLlThP(n)(rpm) = ______ %
10 s = 250 ª.Án = 45 (P×svhúWôd)V = ______Á/¨ªPm
11 Is : Vm = 25 : 1n =_____(P×svhúWôd)Is = úWd ¥WôYpVxm = vhúWôd¡uúYLm / ̈ ªPm
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Vm = 10 Á/¨ªPm
n = 12.5 / ¨ªPm
úWd ¥WôYp = ______
13 ¡Wôe¡u ®hPm =100 ª.Á
úWd vÀÓ = 12 Á/¨ªPm
¡Wôed 'n'' = _____rpm
14 v®u¥p'n' = 250 rpm
vhúWôd¡u NWôN¬úYLm= 30 Á/¨ªPm
vhúWôd¡u ¿[m= ________ ª.Á
15 Lô¬u úYLm= 90¡úXôÁhPo / aYo
¨ßjR GÓjÕdùLôiP úSWm= 10ùNLih
G§oØÓdLm =________ ÁhPo/ùNLih2
16 Lô¬u úYLm = 80¡úXôÁhPo / aYo
¨ßjR GÓjÕdùLôiP çWm = 60ÁhPo
Lô¬u G§oØÓdLm= ________ ÁhPo/ùNLih2
17 G§oØÓdLm= 4.5ÁhPo/ùNLih2
¨ßjR GÓjÕdùLôiP çWm = 50ÁhPo
Lô¬s §ûN úYLm =________ ¡Á/U¦
18 Lô¬p ùNu\çWm = 600¡úXôÁhPo
GÓjÕdùL ôiPúSWm = 8 U¦ 20¨ªPmNWôN¬ §ûN úYLm =________ ¡Á/U¦
19 NWôN¬ §ûN úYLm= 56.3 ¡Á/U¦
ùNu\ çWm = 464.475 ¡.Á
GÓjÕd ùLôiPúSWm = ______ U¦
20 Lôo NdLWm
n = 720 rpm
YhPY¥Y úYLm =18.84 Á/ùNLih
d = ________
21 úLôQ úYLm
n = 2000 rpm
úLôQ§ûN úYLm =_______ úW¥Vu/ùNLih
TVuTÓjÕ
W = 2πN/60 úW¥Vu/ùNLih
22 ©vP²u §ûN/úYLm
S = 74 ª.Á
n = 4500 rpm
CûP §ûN úYLm = _______ ÁhPo/ùNLih
A§LThN §ûN úYLm = _______ ÁhPo/ùNLih
(©vP²u NWôN¬ úYLm)
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12
23 ¨ßjR GÓjRd ùLôiP ùUôjR çWm
(TVuTÓjRÜm = V2/2a)
V = YôL]j§u úYLm= 80 km/hr
G§oØÓdLm = 5 ÁhPo/ùNLih2
Yi¥ JhÓTY¬u ùNVp úYLj§\u = 2 ùNLih
¨ßjR GÓjÕd ùLôiP çWm = _______ ÁhPo
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úYûX«u AXÏ, §\u Utßm Bt\p, Cu_÷²u ϧûWj§\u UtßmCVk§W XôTm T«t£ 1.10.29
F - ®ûN ApXÕ GûP ®ûN, ̈ ëhP²p ( N)
s - ®ûNVôp JÚ ùTôÚs SLÚm çWm
t - úSWm ùNLi¥p
v - úYLm ÁhPo / ùNLih
w - ®ûNVôp JÚùTôÚs úYûX ùNnRp (A)SLÚRp _øpv£p
P - §\u Yôhv£p
Pout - §\u ùY°lTôÓ (Power output)
Pin - §\u EsÇÓ (Power input)
®ûN (Force)
®ûN GuTÕ, JÚ ùTôÚ°u ÁÕ ùNVpThÓAk¨ûXûV Uôtß¡\úRô ApXÕ Uôt\ØVp¡u\úRô AûR ®ûN Gu¡ú\ôm
®ûN = ¨û\ X ØÓdLm
F = Ma
AXÏ (Unit)
®ûN = ¨û\ X ØÓdLm (F = M x a)
= ¡úXô X ÁhPo (kg X m/sec2 )
= 1 ¨ëhPu (SI unit)
¨ëhPu : 1 ¡úXô ¨û\Ùs[ JÚùTôÚ°u ÁÕ ùNVpThÓ, 1 ÁhPo/ ùNLih2 ØÓdLjûR HtTÓjÕm®ûN 1 ¨ëhPu BÏm.
FPS = 1 TÜiÓ X 1 A¥/ùNih2
= 1 TÜiÓ
Cus = 1 ¡Wôm X 1ùN.Á/ ùNLih2
= ûPu
Mks = 1 ¡úXô X 1ÁhPo/ùNLih2
= ¨ëhPu
1 ̈ ëhPu = 105 ûPuv
1 ¡úXô GûP= 9.8 1N (¨ëhPuv)
1 TÜiÓ = 4.448N (¨ëhPuv)
¨ëhPu = 0.225 TÜiÓ
úYûX (Work) (TPm 1)
®ûNVôp ùNnVlTÓYûR úYûX Gu¡ú\ôm.‘F’ Gu\ JÚ ®ûN JÚ ùTôÚ°u ‘S’ çWmSLoYÕ úYûX G]lTÓm.
úYûX (Work done) ‘W’ = F x s.
úYûX = ®ûN«u U§l× x SLÚm çWm
úYûX«u AXÏLs
A¡X EXL RW ¨oQV Øû\ (S.I system)
JÚ ¨ëhPu ®ûNVô]Õ JÚ ùTôÚ°uÁÕ ùNVpThÓ AlùTôÚû[ 1 ÁhPo çWmSLoj§]ôp ùNnVlThP úYûX 1 _øp(Joule)BÏm
BûLVôp _øp = 1 ¨ëhPu x 1 ÁhPo = 1¨ëhPu ÁhPo (Nm)
AúR úTôp 1 _øp = 1 Nm = 105 ûPuv x 100ùN.Á = 107 ûPuv ùN.Á
= 107 Godv
Nôo©Xô AXÏ (Absolute units) (TPm 2)
C.G.S. ùUh¬d Øû\«p úYûX«u AXÏ = 1God = 1 ûPu x 1 ùN.Á
F.P.S ùUh¬d Øû\«p úYûX«u AXÏ = 1×h TÜiPp = 1 TÜiPp x 1 A¥
M.K.S. ùUh¬d Øû\«p úYûX«u AXÏ = 1_øp = 1 ¨ëhPu x 1 ÁhPo
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YûWVßdLlThP AXÏLs (Derived units)
C.G.S. (ùUhôõd) Øû\«p 1 ¡Wôm GûP x 1ùN.Á = 981 Gôódv
F.P.S. (©ôõh¥x) Øû\«p 1 A¥ TÜiÓ = 981×h TÜiPp
M.K.S. (ùUhôõd) Øû\«p 1 ¡úXô GûP (A) 1¡úXô ®ûN = 981 _øp
Bt\p (Power) (TPm 2)
úYûX ùNnVlTÓm ÅRúU §\u G]lTÓm.
JÚ YôhÓdÏ GÕ NUm Bt\≠u Yôhv = W/t = F.s/t = F x V
M.K.S. (ùUhôõd) Øû\«p AXÏ 1 kgf ÁhPôó/ùNLih JÚ Ï§ûW §\u = 75 ¡úXôÁhPôó/ùNLih ApXÕ 4500 kgf ÁhPôó/¨ªPm.
1ϧûW §\u (HP) (ùUhôõd) = 735.5 Yôhv
1ϧûW §\u (HP) (©ôõh¥x) = 746 YôhvLs= 0.746 ¡úXô Yôhv
1 ¡úXô Yôhv = 1.34 ϧûW §\u (HP)
CVk§WeLs úYûX ùNnYRtÏùNÛjRlTÓm Bt\p (Input) Cu×h Bt\pG]lTÓm. Gk§Wj§p CÚkÕ ¡ûPdÏmBt\p AÜh×h (output) Bt\p G]lTÓm.CVk§Wj§p Es[ Cu×h Bt\ûX®PAÜh×h Bt\p EWôn®u LôWQUôLÏû\YôLúY CÚdÏm. Cu×h Bt\ÛdÏmAÜh×h Bt\ÛdÏm CûPúV Es[ ®¡RmGk§Wj§u §\û]l ùTôÚjRÕ. CÕNR®¡Rj§p á\lTÓ¡\Õ. (TPm 3)
¾ôóUô²dLlThP ϧûWj§\u UtßmTVuTÓjRlTÓm ϧûWj §\u (IndicatedHorse Power and Brake Horse Power)
JÚ CVk§Wm GqY[Ü §\àPuùNVp×ôõVdá¥VÕ GuTÕ LQd¡Vp ôö§VôLYûWVßdLlThÓ, CVk§Wj§pùTôÚjRlThÓs[ ®TWj RLh¥pϱdLlTÓm. CÕúY ¾ôóUô²dLlThPϧûWj §\u G]lTÓm. CûY ÑÚdLUôLI.H.P. G]lTÓm
JÚ CVk§Wm CVeÏmúTôÕ, HtTÓmEWônÜj RûPL[ôp CZkRÕúTôL, Á§TVuTÓjRlTÓm, ϧûWj §\û]d ϱdÏm.CûR ÑÚdLUôL B.H.P G]lTÓm. CÕ I.H.P.§\û] ®P Ïû\YôL CÚdÏm.
®ûNVôp HtTÓm úYûX = ®ûN«u A[Üx ùTôÚs SLoókR çWm
§\u = Total work done / total time taken
Bt\p (Energy)
ùTôÚsLs úYûX ùNnV úRûYVô]§\ûUdÏ Bt\p Guß ùTVôó. CÕ §\uúSWj§tÏ NUUôL CÚdÏm. JÚ ùTôÚ°uBt\p, AÕ ùNnVdá¥V úYûXûVdùLôiÓ A[®PlTÓ¡\Õ. G]úYúYûX«u AXÏL[ôúXúV Bt\pA[®PlTÓ¡\Õ.
Bt\≠u YûLLs (Forms of energy)
CVk§W Bt\p (Mechanical energy), ªu Bt\p(Electrical energy), AÔ Bt\p (Atomic energy),ùYlT Bt\p (Heat energy), J° Bt\p (Lightenergy), úY§ Bt\p (Chemical energy), J≠ Bt\p(sound energy). JÚ YûL Bt\ûX Utù\ôÚYûL Bt\XôL Uôt\Xôm.
Bt\p A¯®uûU ®§ (Law of conservationof energy)
– Bt\ûX BdLúYô ApXÕ A¯dLúYôCVXôÕ.
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– JÚ ùTôÚ°p Es[ ùUôjR Bt\ÛmA§úXúV CÚdÏm. (TPm 4)
JÚ ùTôÚ°u CÚdÏm ̈ ûX (A) CVdLj§pEs[ ùTôÚ°p APe¡Ùs[ CVk§WBt\p, ¨ûX Bt\XôLúYô (A) CVdLBt\XôLúYô CÚdLXôm.
¨ûX Bt\p (Potential energy)
JÚ ùTôÚ°p úNªjÕ ûYdLlThP ApXÕAlùTôÚs CÚdLdá¥V ¨ûX«uLôWQUôLl ùT\dá¥V Bt\p, ̈ ûX Bt\pG]lTÓm (TPm 4). JÚ ùTôÚ°u ¨û\ ‘h’EVWj§p ûYdLlThÓs[Õ. AûRA¥lTûPVôLd ùLôiÓ ¨ûX Bt\pL¦dLlTÓ¡\Õ. AÕ mgh ApXÕ Wh ApXÕFh ARôYÕ W ApXÕ F CûY ®ûN«uGûPVôÏm ùTôÚû[ ¸úZ ®ÓYRtÏAàU§jRôp Fh I TVuTÓj§ ̈ ûX Bt\ûXLiÓ©¥dLXôm.
ERôWQm
• ùRôh¥«p úRd¡ ûYdLlThP ¿ôó
• AÝjRlThP ÑÚs ®p
CVdL Bt\p (Kinetic energy)
JÚ ùTôÚs CVeÏYRu êXm ùT\dá¥VBt\p, CVdL Bt\p G]lTÓm. JÚùTôÚ°u ̈ û\ ‘m’ KnÜ ̈ ûX«p BWm©jÕ‘F’ Gu\ ®ûN«u êXm ‘s’ çWjûR LPdL ‘v’Gu\ §ûNúYLjûR AûP¡\Õ. CR]ôpùTôÚs ùNnR úYûX = F x s B]ôp F = m x aG]úY ùTôÚs ùNnR úYûX = m x a x s.
B]ôp a x s = Hù]u\ôp ùTôÚs KnÜ
¨ûX«p CÚkÕ ×\lTÓ¡\Õ.
BûLVôp ùTôÚ°u úYûX = .
ùTôÚ°u úYûX = ùTôÚs ùTt\ Bt\p
CVdL Bt\p = .
ùTôÚs ùTt\ Bt\p = ùTôÚ°u úYûX
¨ûX Bt\p = mgh
CVdL Bt\p = mv2
¨ûX Bt\p = CVdL Bt\p (EWônÜR®odLlThPôp).
ERôWQm
• úWô≠e YôL]m (Rolling vehicle)
• ÑZÛm ©û[ Åp (Rotating fly wheel)
• KÓm ¿o (Flowing water)
• ¸úZ ®Ým ùTôÚs (Falling weight)
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¨ûX Bt\p, CVdL Bt\p Utßm AYt±tÏ ùRôPo×ûPV LQdÏLsUtßm §\]ônÜ T«t£ T«t£ 1.10.30
¨ûX Bt\p (Potential energy)
‘h’ EVWj§p CÚkÕ Ñj§«u RûX ¸úZ®Ý¡u\Õ. .
¨û\ (m) = 10 ¡úXô.
EVWm (h) = 1.4 ÁhPôó
V2 = 2 gs
V2 = 2 x 9.81 x 1.4
V2 = 27.468
V2 = 5.24 Á/ùNLih
= 10 ¡úXô x 9.81 ÁhPôó/ùNLih2 x 1.4 ÁhPo(TPm 1)
= 137.3 ¨ëhPu ÁhPôó ( 1N = 1kg.m/sec2)
úYûX = ®ûN«u U§l× x SLÚm çWm
work done= F x s = 900 x 10 ¨ëhPu ÁhPôó
= 9000 ¨ëhPu ÁhPôó = 9000 _øp
TYo =
• 2000 kgf TÞûY, 2 ÁhPôó /ùNLih úYLj§pEVôójR úRûYVô] ϧûWj §\û]LQd¡ÓL. TVàߧ\u 70%.
≠lh -I 1 ùNLih¥p EVojR ùNnR úYûX
®ûN = 2000 kgf
úYûX = F x d
§\u
= 4000 w
§\u ùY°lTôÓ = 4000 w
§\u EsÇÓ = §\u ùY°lTôÓ
η =
EsÇÓ §\u = 7.6 HP
• 100 ¡Wôm ̈ û\, 10 ÁhPôó EVWj§p CÚkÕ¸úZ ®Ý¡u\Õ. CR]ôp AlùTôÚÞdÏHtTÓm CVdL Bt\p GqY[Ü. (g «uU§l× ÁhPôó /ùNLih2 G]d ùLôsL.
BWmT §ûN úYLm= 0
LPkR çWm 10 ÁhPôó
Cߧ §ûN úYLm2
=V2 = 2 x a x s = 2 x 10x10 ÁhPôó2//ùNLih2
CVdL Bt\p (K.E) = x 10 ¡úXô x 5.242
= 137.3 ̈ ëhPu ÁhPôó
ERôWQeLs (Examples)
• JÚ Ll© 900 ¨ëhPu ®ûNÙPu á¥V¨û\ûV 10 ÁhPôó EVWj§tÏj çdL 2¨ªPm GÓjÕd ùLôs¡\Õ. ®ûNVôpHtThP úYûX Utßm Bt\ûXÙmLiÓ©¥.. (TPm 2)
=75 _øp
ùNLih75 Yôhv
ùY°lTôÓEsÇÓ
x 100%
W t
=9000 _øp
120 ùNLih
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YôL]j§u ̈ ûXVô] úYLjRôp CVdLBt\p A§Lôõd¡u\Õ. (K.E. developed bythe vehicle at a constant speed)
• JÚ Pu GûPÙs[ JÚ úUôhPôo YôL]mU¦dÏ 60 km/hr úYLj§p ùNp¡\Õ. CkRúYLj§p ARu CVdL Bt\ûX LQd¸ÓùNn.
YôL]j§u CVdL Bt\p = mv2
ARôYÕ m = JÚ Pu ApXÕ 1000 ¡úXô
v = 60 km/hr
¾ôóÜ
v þI ÁhPôó/ùNLihPôL Uôt\ AR]ôpSUdÏ ¡ûPlTÕ
( 1km = 1000m)
( 1hour = 3600sec)
YôL]jûR ØÓdLm ùNnÙm ùTôÝÕCVdL Bt\p A§LôõdÏm (K.E.developed bya vehicle during acceleration)
• 1200 ¡úXô ¨û\ Es[ JÚ úUôhPôóYôL]m 36 ¡úXô ÁhPôõp CÚkÕ 48 km/hrdÏ úYLj§tÏ A§LôõdL ØÓdLmùNnVlTÓ¡\Õ. ØÓdLj§u ùTôÝÕHtTÓm A§L CVdL Bt\ûX LQd¡PÜm.
¾ôóÜ
YôL]j§u ¨û\ = 1200 ¡úXô
YôL]j§u CVdL Bt\≠u úYLm 36 ¡Á/U¦.
= x 1200 x 362J
CVdL Bt\p KE= mv2 J
v= 36 ¡Á/U¦ =36 x = 10 Á/ùNLih
YôL]j§u CVdL Bt\p 48 ¡Á/U¦úYLj§p
= x 1200 x 482J ( 1 ¡úXô¡Wôm ÁhPo /
ùNLih2 = 1N)
( 1 ¨ëhPu ÁhPo = 1 _øp)
v= 48 ¡Á/U¦ =48 x= Á/ùNLih
CVdL Bt\p = x1200 x 10 x10=60000J
CVdL Bt\p = x1200 x x =106666.67 J
CVdL Bt\p ®j§VôNm = 106666.67 J - 60000J = 46666.67 J = 46.666 KJ.
YôL] CVdLj§u úTôÕ HtTÓm úYûX(Workdone in vehicle operation)
úUôhPôó YôL]m NôûX«p CVeÏYRtÏùNnÙm CVk§W úYûX CWiÓ YûLVôL©ôõdLlTÓ¡\Õ.
– IC Cg£u úYLm Utßm TÞûYÙmLY]j§p ùLôiÓ ØÝ Bt\ûXùY«lTÓjR ùNnVlTÓm úYûX.
– úUôhPôó YôL]m TX ®RUô]ùNVpTôÓL°p, NôûX«p DÓTÓmùTôÝÕ ARôYÕ, Ïu±uÁÕHßmùTôÝÕ-/ ØÓdLm /©úWd¡e /CÝjÕf ùNpÛRp (towing) Utßm©uú]ôdÏ ùNpÛRp B¡VYt±pùNnVlTÓm úYûX.
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§\]ônÜ T«t£ (Assignment)1 ¨û\ (m)= 55 kg
a) s = 1.82 ªhPoGûP (W) = _______øp (joules)b) s = 1.40 ÁhPoGûP (W)= _____øp (joules)c) s = 0.85ÁhPoGûP (W) =_øp(Joules)
2 úSWm(t)= 8 ùNLiha) §\u (P) = _____Yôhvb) §\u (P) = _____Yôhvc) §\u (P) = _____Yôhv
3 GûP (W) = 1312.5_øp¨û\(m) = 350 ¡úXô¡Wômç W m ( s ) = _ _ _ _ _ÁhPo
4 ¨û\ (m) = 75 ¡úXôçWm (s) = 100 metresGûP (W) = ______¨ëhPu ÁhPo§\u (P) = ______Yôhv
5 V = 1 Á3/ùNLihH = 2 Áη = 0.75EsÇÓ §\u =_____ ¡úXôYôhv
6 § \ u ( P ) = 1 2¡úXôYôhvçWm (s) = 4 ÁhPôóúSWm (t) = 20 secs¨û\ (m)=______¡úXô
7 ®hPm (d) = 3 metreEVWm (H) = 2 metreúSWm (t) = 20 minutesçWm (s) = 6 metresP = ______ kWù R ô h ¥ « pR i ½ o¨WlThÓs[ÕTm©e EVWm (s)
8 ®hPm (d) = 200 mmGi¦dûL (n) = 750rpm®ûN (F) = 700¨ëhPu§\u (P) = _____¡úXô Yôhv
9 Cu×h §\u (P) (input) = 4 ¡úXô Yôhv AÜh×h §\u (P) (output)
=3450_øp/ùNLih η = ______ %
10 Ri½¬u L]A[Ü
L] A[Ü (‘V’) = 10metre3
EVWm (H) = 18 metres úSWm (t) = 20 sec η = 70 %(P) AÜh×h (output)= ______ ¡úXôYôh
11 ®hPm (d) = 225 mm çWm (s) = 450 mm© v P ² uAÝjRm
‘P’ = 4.5 bar L] A[Ü (V) = 2.5ÁhPo/ùNLih
(©vPu úYLm) η = 70 % Cu×h §\u
=_____ ¡úXô Yôh
12 TmlùNnVlhPRi½o (‘V’)
= 3 metre3/min
EVWm (H) = 6 metre
η = 0.8
Cu×h §\u
= ______ ¡úXôYôh
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ùYlTm Utßm ùYlT¨ûX LÚjÕÚ, ùYlTj§u ®û[ÜLs,ùRoúUôÁhPo vúLp, ùNp£Vv, @TôWu aöh, ìUo, ùLp®u UtßmùYlTm Utßm ùYlT¨ûXdÏ CûPúVVô] úYßTôÓLs
T«t£ 1.11.31
ùYlTm (Heat)
ùYlTm GuTÕ JÚ YûL Bt\p. ùYlTBt\ûX úYß Bt\XôL Uôt\Xôm ùYlTmãPô] Tϧ«p CÚkÕ Ï°okR TϧdÏSLÚm.
ÑV ùYlT Ht×j §\u (A) ùYlT Gi(Specific heat)
JÚ ùTôÚ°u ÑV ùYlT Ht×j §\u GuTÕJÚ ¡Wôm ¨û\Ùs[ JÚ ùTôÚ°uùYlT¨ûXûV 1°C EVojÕYRtÏúRûYlTÓm ùYlTj§u A[Ü BÏm.
ÑV ùYlT Ht×j §\u ‘s’ Gu\ GÝj§pϱl©PlTÓ¡\Õ.
Ri½¬u ÑV ùYlT Ht×j§\u = 1
AÛª²Vm = 0.22
ùNm× = 0.1
CÚm× = 0.12
ùYlT Ht×j §\u (Thermal capacity)
JÚ ùTôÚ°u ùYlT ¨ûXûV 10CEVojÕYRtÏ úRûYVô] ùYlTmAlùTôÚ°u ùYlT Ht×j§\u G]lTÓm.
ùYlT Ht×j§\u = ms LúXô¬
m = ùTôÚ°u ̈ û\ ¡Wôªp
s = ùYlT Gi
LúXô¬@©d U§l× (Calorific value)
JÚ Ï±l©hP ̈ û\Ùs[ JÚ G¬ ùTôÚû[Øt±Ûm G¬dÏm úTôÕ ùY°lTÓm ApXÕEtTj§VôÏm. ùYlTm AlùTôÚ°uLúXô¬@©d úYpë (Calorific value) G]lTÓm.
¿oNU¨ûX (Water equivalent)
JÚ ùTôÚ°u ¿oNU¨ûX GuTÕ ùTôÚû[1°C ùYlT¨ûXûV EVojRúYô (A )Ïû\dLúYô ùNnÙm úTôÕ AlùTôÚ°pAPe¡Ùs[ ¿Wô]Õ AlùTôÚû[lúTôXúY ùYlTjûR Eh ¡W¡dLúYô (A)ùY°«PúYô ùNn¡\Õ. AÕúYAlùTôÚ°u ¿oNU¨ûX G]lTÓm.
¿oNU¨ûX = ¨û\ x ùYlT Gi
G]úY (Water equivalent = Mass of the substance xspecific heat of the substance)
ùYlTj§u YûLLs (Types of heat)
1 EQWlTÓm ùYlTm (Sensible heat)
2 Es Uû\ ùYlTm (Latent heat)
ùYlTj§u AXÏLs (Units of heat)
LúXô¬ (Calorie)
JÚ ¡Wôm ̈ û\Ùs[ ¿¬u ùYlT ̈ ûXûV 1°ùNu¥¡úWh (1°C) EVojÕYRtÏ úRûYVôLùYlTm 1 LúXô¬ BÏm.
BTHU: JÚ TÜiÓ ¨û\Ùs[ ¿¬u
ùYlT¨ûXûV 1° TôWuÍhÓdÏ (1°F)EVojÕYRtÏ úRûYVô] ùYlTm 1 BTHUG]lTÓm. (CÕ ©¬h¥x ùRoUp ë²hBÏm)
C.H.U: JÚ TÜih ¨û\Ùs[ ¿¬uùYlT¨ûXûV 1°C EVojÕYRtÏúRûYlTÓm ùYlTm 1 C.H.U G]lTÓm.
_øp (Joule)
_øp GuTÕ S.I. Øû\«p ùYlTj§uAXLôÏm.
1 LúXô¬ = 4.186 _øp
ùYlTj§]ôp HtTÓm ®û[ÜLs (Effectsof heat)
• ùYlT¨ûX Uôt\m (Change in temperature)
• EÚY A[®p Uôt\m (Change in size)
• ¨ûX Uôt\m (Change in state)
• LhPûUl©p Uôt\m (Change in structure)
• CVp©Vp RuûU«p Uôt\m (Change inPhysical properties)
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1 EQWlTÓm ùYlTm (Sensible heat)
JÚ ùTôÚ[ô]Õ ùYlTjûR CZkúRô (A)Htú\ô Ru ¨ûX Uô\ôUp ùYlT ¨ûX«pUhÓm Uôt\m AûPkRôp AkR ùYlTmEQWlTÓm ùYlTm G]lTÓm. CûRùRoúUô ÁhP¬p LôQlTÓm ùYlT¨ûX®j§VôNjûR ûYjÕ LiLô¦dLXôm.
2 Es Uû\ ùYlTm (Latent heat)
JÚ ùTôÚ[ô]Õ ùYlTjûR CZkúRô (A)Htú\ô ùYlT ¨ûX Uô\ôUp ARu ¨ûXUhÓm Uôt\m AûPkRôp AkR ùYlTmEsUû\ ùYlTm G]lTÓm. C§p HtßdùLôs[lThP ùYlTúUô (A) CZkRùYlTúUô ùTôÚ°p ùYlT¨ûX Uôt\jûRHtTÓjRôÕ.
YûLLs
1 ùTôÚ°u EÚÏR≠u Es Uû\ ùYlTm(Latent heat of fusion of solid)
2 ùTôÚ°u EÚÏR≠u B®VôYRu EsUû\ ùYlTm (Latent heat of vaporisation of solid)
1 ùTôÚ°u EÚÏR≠u Es Uû\ùYlTm (Latent heat of fusion of solid)
1 ¡Wôm ̈ û\Ùs[ JÚ ùTôÚû[ ARu EÚϨûX«p ùYlT ¨ûX Uô\ôUp Øt±Ûm¿oU ¨ûXdÏ UôtßYRtÏ úRûYVô]ùYlTm AlùTôÚ°u EÚÏR≠u Es Uû\ùYlTm G]lTÓm.
CRu AXÏ LúXô¬/ ¡Wôm
T²dLh¥«u EÚÏR≠u Es Uû\ùYlTm (Latent heat of fusion of ice)
1 ¡Wôm T²dLh¥ûV 00C ùYlT ̈ ûX«úXúVØt±Ûm ¿WôL UôtßYRtÏ úRûYVô]ùYlTm T²dLh¥«u EÚÏR≠u EsUû\ùYlTm G]lTÓm.
T²dLh¥«u Es Uû\ ùYlTm (L) =80 LúXô¬/ ¡Wôm
2 B®VôR≠u Es Uû\ ùYlTm (Latentheat of vapourisation of liquid)
JÚ ¿oUm ARu ùLô§¨ûX«p HtTÓmùYlTm ARû] B®VôdL UhÓúUTVuTÓ¡\Õ. CkR ùYlTm B® ¨ûX«pUû\kÕ CÚlTRôp CÕ B®VôR≠u EsUû\ ùYlTm G]lTÓm.
¿oUj§u B®VôR≠u EsUû\ ùYlTm(Latent heat of vaporisation of water or latent heat ofsteam)
1 ¡Wôm ¿Wô]Õ ARu ùLô§ ¨ûX«pùYlT¨ûX Uô\ôUp Øt±Ûm B®VôRÛdÏúRûYVô] ùYlTj§u A[Ü AkR ¿oUj§uB®VôR≠u EsUû\ ùYlTm G]lTÓm.
B®«u Es Uû\ ùYlTm (L) = 540 LúXô¬/¡Wôm
ùYlT¨ûX (Temperature)
JÚ ùTôÚs ãPôLúYô (A) Ï°of£VôLúYôCÚdÏm ùYlT A[úY ARu ùYlT ¨ûXBÏm. CÕ ùYlTUô²ûVd ùLôiÓA[dLlTÓ¡\Õ.
ùYlT¨ûXûV A[dÏm vúLpLs (Tem-perature Scales)
ùYlT¨ûX CWiÓ ̈ ûXVô] ùW@lTWuv×s°L[ô] Juß Ri½o Eû\Ùm ×s°Utù\ôuß Ri½¬u ùLô§ ¨ûX×s°LÞdÏ CûPúV A[Üj§ÚjRm
(caliberated) ùNnVlTÓ¡\Õ vúLpL°p Es[
AkR ¨ûXl×s°L[ôY].
vúLp Eû\¨ûX ùLô§¨ûXScale Freezing point Boiling point
ùNu¥¡úWh (°C) 0°C 100°C
@TôWuÍh(°F) 32°F 212°F
ùLp®u 273°K 373°K(K)
ìUo (°R) 0°R 80°R
ùYlTm GuTÕ JÚ ®R Bt\p.ùTôÚ°u ãÓ, (A) Ï°of£ ̈ ûXûVϱlTÕ ùYlT¨ûXVôÏm. JÚùYlT¨ûX vúLûX Utù\ôÚùYlT¨ûX vúLXôL Uôtß
YRtLô] E\ÜLs
ùLô§¨ûX (Boiling point)
JÚ ùTôÚs ùYlTjRôp §WY ¨ûX«pCÚkÕ YôÙ ̈ ûXdÏ UôßYÕ AlùTôÚ°uùLô§¨ûX G]lTÓm.
Ri½¬u ùLô§ ̈ ûX 1000C.
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.11.31
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EÚÏ ¨ûX (Melting point)
JÚ ùTôÚs ùYlTjRôp §P ̈ ûX«≠ÚkÕEÚ¡ §WYUôL UôßYÕ ApXÕ §WYmÏ°okÕ §Pl ùTôÚ[ôL UôßYÕAlùTôÚ°u EÚÏ ¨ûX G]lTÓm.
Iv£u EÚÏ ¨ûX 00C
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.11.31
ùYlTm Utßm ùYlT¨ûXdÏ CûPúV Es[ ®j§VôNm
(Difference between heat and temperature)
ùYlTm (Heat) ùYlT¨ûX (Temperature)
1 CÕ JÚ YûL Bt\p ùYlTj§u ̈ ûXûV ùR¬®d¡u\Õ.
2 CRu AXÏ LúXô¬ CRu AXÏ ¥¡¬
3 LúXô¬ ÁhPWôp ùYlTm ùYlTUô²Vôp ùYlT¨ûXA[dLlTÓ¡\Õ A[dLlTÓ¡\Õ
4 CWiÓ ùTôÚhL°u ùYlTjûR CWiÓ ùYlT¨ûXûV áhÓYRuáh¥ ARu ùUôjR ùYlTjûR êXm LXûY«u ùYlT¨ûXûVLQd¡P Ø¥Ùm. LiÓ©¥dL CVXôÕ.
5 JÚ ùTôÚû[ ùYlTlTÓjÕm CWiÓ ùTôÚhL°u ùYlT¨ûX JúWùTôÝÕ ùYlT¨ûX EVoÜdÏ Uô§¬VôL CÚkRôÛm AûYL°uAlTôtThÓ ùYlT A[Ü ùYlT A[Ü ®j§VôNUôL CÚdÏm.A§L¬dÏm.
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100
ùYlT¨ûXLû[ ùNu¥¡úWÓ, @TôWu aöh, ìUo, ùLp®u B¡VvúLpL°p Uôt\m ùNnRp T«t£ 1.11.32
1 00 C - I 0F BL UôtßL
100
C
180
32F 00
=−
180100
C32F
00 ×=−
180100
032F0 ×=−
°F = 0 + 32
= 320F
00C = 320F
2 -400 C - I 0F BL UôtßL
100
C
180
32F 00
=−
180100
C32F
00 ×=−
180100
4032F0 ×
−=−
F - 32 = -72
°F = -72 + 32
= -400F
-400C = -400F
3 370 C - I K BL UôtßL
100
273K
100
C 00 −=
°K-273 = C
°K = C + 273
°K = 37 + 273
= 310 K
370C = 310K
4 700 C - I ìUo BL UôtßL
80
R
100
C 00
=
80100
CR0 ×=
5680100
70R0 =×=
700C = 560R
5 -250 F - I 0C BL UôtßL
180
32F
100
C 00 −=
180
3225
100
C −−=
°
100180
57-C0 ×=
31.669
285C0 −=
−=
- 250F = -31.70C
6 98.60 F - I 0C BL UôtßL
100180
32FC
00 ×
−=
100180
3298.6C0 ×
−=
100180
66.6×=
C37180
6660 0==
98.60F = 370C
§\]ônÜ T«t£ (Assignment)
¸rLiPûYLû[ UôtßL
1 10.50C = ___0F
2 400C = ___0F
3 600C = ___0F
4 800C = ___0F
5 1050C = ___0F
6 -1000C = ___0F
7 770F = ___0C
8 200F = ___0C
9 4280F = ___0C
10 -2100F = ___0C
11 720R = ___0C
12 1430C = ___K
13 3730K = ___0C
14 7460K = ___0F
15 GkR ùYlT¨ûX«p @TôWu aöhùYlTUô²«u A[Ü ùNu¥¡úWÓùYlTUô²«u A[ûYlúTôp CWiÓUPeÏ CÚdÏm.
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101
ùYlT¨ûXûV A[dÏm LÚ®Ls, ùYlTUô²«u YûLLs,ûTúWôÁhPo Utßm ùYlT T¬Uôt\m T«t£ 1.11.33
ùYlT Bt\ûX A[®ÓRp (Measuring heatenergy)
Bt\p, úY§«Vp ®û[ÜLs êXm, JXõ,J≠ (A) ªu]ôt\p BL Uôt\lTÓ¡\Õ.B]ôp ùTÚmTôÛm ùYlT Bt\XôL Uôt\lTÓ¡\Õ. CRu êXm GqY[Ü ùYlT Bt\pUôt\lThPÕ GuTûR A[dLXôm.
ùRôPeÏ¡\Õ ARôYÕ -273°. ùYlT¨ûXCûPùY°Ls AúR Uô§¬ CÚdÏm.
∴ 273K = 0°C, 20°C = 273K + 20K = 293K.
LÚ®Ls (Instruments)
ùTôÚsL°p HtTÓm RuûU Uôt\mªuNôWjRôp ùTôÚhL°u ùYiûUVôLG¬¡u\ úRôt\m, ùYlTdL§o ÅNp UtßmEÚÏRp B¡V UôßRûX LQd¡p ùLôiÓLÚ®Ls ùYlT¨ûXûV A[ùYÓjÕT¥lTRtÏ ERÜ¡\Õ.
ùYlT¨ûXUô² (Thermometer)
§Pl ùTôÚs Utßm §WYjûR ùYlTlTÓj§]ôp AlùTôÚs ®¬YûPÙmClTi©û] A¥lTûPVôLd ùLôiÓùYlTUô²Ls AûUdLlTÓ¡u\]. TôRWNm(Mercury) Utßm BpLaôp (alcohol)B¡VûYLs ºWô] A[®p ®¬YûPÙm.ùYlTjûR ùNÛj§]ôp §WYj§u L]A[Ü A§L¬dÏm úTôÕ Utßm úLl©pX¬¥ë©p (capillary tube) §WYm EVo¡u\Õ.ùTôÕYôL CkR YûL ùYlT¨ûXUô²«pTôRWNm TVuTÓjRl TÓ¡\Õ. Hù]u\ôpTôRWNUô]Õ LiQô¥ ¥ë©p JhPôÕ,(K°ÅÑm) 3000c YûW A[dLXôm.
ûTùUhPp (bimetal) ùYlT¨ûX Uô²«uEúXôLm ùYqúYß ùYlT ùTÚdL GiùLôiPÕ. CkR ûTùUhPp, vûTWp (spiral)Y¥®p Yû[dLlThÓ (twisted) CÚdÏm.ùYlT¨ûX EVÚm úTôÕ CÕ ÑÚs ÑÚ[ôLEVÚm.
ùYlTd LXûYûV A[dÏm LÚ®ûV LúXô¬ÁhPo Guß AûZd¡ú\ôm. CÕ EÚû[Y¥®p Es[ Tôj§Wm BÏm. LXdÏm LWi¥(stirrer) ùTôÕYôL ùNm× EúXôLjRôpùNnVlTh¥ÚdÏm.
JÚ LúXô¬ ÁhP¬p ãPô] §P/§WYùTôÚhLû[ Ï°okR ¨ûX«p Es[ §P/§WY ùTôÚsLÞPu LXdÏm ùTôÝÕ,CWiÓ ùTôÚsLÞm ùYlT¨ûXûVAûPÙm YûW ùYlTlT¬Uôt\m ¨LÝm.AúR LúXô¬ ÁhP¬Ûm AúR ùYlT¨ûXA[®tÏ UôßRp HtThÓ CÚdÏm. LXdÏm®§«u T¥,
§P/ §WY ùTôÚ°u CZkR ùYlTm = §P /§WY ùTôÚhL°u HtLlThP ùYlTm +LúXô¬ ÁhP¬p HtThP ùYlTm
⎥⎦
⎤⎢⎣
⎡
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
⎥⎥⎥
⎦
⎤+
rcalorimeteby
edHeat absorb
substance
idsolid / liqu
ed byHeat absorb
liquid
by solid/
Loss of heat
A[®ÓRp (Measurement)
ùYlT¨ûX ùTôÕYôL ¥¡¬ ùNp£V³pA[dLlTÓ¡\Õ. CmØû\«p Ri½¬uEû\ ̈ ûX 0°C Utßm Ri½¬u ùLô§ ̈ ûX100°C Gußm YûWVßdLlThÓs[].ùLp®u ùYlT¨ûX vúLp absolute 0° p
ûTúWôÁhPo (Pyrometer)
TX YûLVô] EúXôL JVÚdÏm Tt\ ûYdÏm×s°dÏm CûPúV ùYlTjûR EiPôdÏmúYôphúPû_ (voltage) A¥lTûPVôLd
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102
ùLôiÓ ùRoúUô GXdh¬d ûTúWô ÁhPoAûUdLlTÓ¡\Õ. ùYlT A[®u ×s°dÏmUtßm JV¬u Ï°okR Øû]LÞdÏ CûPúVEs[ ùYlT¨ûX ®j§VôNjûR ùTôÚjÕúYôphúP_ó CÚdÏm. ùNm× EúXôLjRôpùRoúUô Ll×s G≠ùUihv (Thermocoupleelements) AûUdLlTÓ¡\Õ. (600°C YûW«p)(A) ©[ôh¥]m Utßm ©[ôh¥]m þúW¥Vm (platinum-rhodium) (1600°C YûW«p)
úW¥úVNu ûTúWôÁhPo, £YkR ùYlTEúXôLj§u 3000°C YûW Es[ ùYlT¨ûXûV A[dLXôm. Ï®dLlThP ùRoUpúWvûN (thermal rays) Bl¥Lp ùXuv êXUôLùRoúUô G≠ùUihÓdÏ (thermo element)@lúTôdLv ùNnV úYiÓm. CmÁhP¬uvúLpLs ¥¡¬ ùNp£Vv (A) ùLp®uAX¡tÏ A[Üj§ÚjRm ùNnVlTÓ¡u\].
ùYlTm TWÜRp êuß YûL°pSûPùTß¡\Õ.
• ùYlTd LPjRp (By Conduction)
• ùYlTf NX]m (By Convection)
• ùYlTd L§o ÅNp (By Convection)
ùYlTdLPjRp (Conduction)
JÚ ùTôÚs Rôu ùTt\ ùYlT Bt\ûXêXd áßLs CPm ®hÓ CPm ùTVWôUpAYt±u CVpTô] ¨ûX«p CÚkÕùLôiúP ùYlTjûR TWYf ùNnÙm Øû\úVùYlTdLPjRp G]lTÓm. ùYlTd LPjRpEúXôLeL°p ¨LÝm. ùTôÚ°uêXdáßL°u SLoúYô ApXÕ Uôt\úUôHÕªu± ùYlTm JÚ Øû]«p CÚkÕUtù\ôÚ Øû]dÏ TWÜm. ùTôÕYôL ªuLPj§Ls JÚ SpX ùYlTd LPj§VôÏm.Utßm SpX ùYlTLôl×Ls SpXªuLPjRôl ùTôÚ[ôÏm. JÚ SpXùYlTLôl×lùTôÚs EVoùYlT¨ûXûVRôeL úYi¥V AY£VªpûX.
ùYlTm TWÜRp (Transmission of Heat)
ùYlTm JÚ YûL Bt\p Utßm úYûXùNnÙm RuûU EûPVÕ. ùYlT¨ûX A§LùYlTm Es[ ùTôÚ°p CÚkÕ RôrYô]ùYlTm Es[ ùTôÚÞdÏ TWÜ¡u\Õ. (A)ùYlT¨ûX A§LUôL Es[ ùTôÚ°≠ÚkÕùYlT¨ûX RôrYôL Es[ ùTôÚÞdÏùYlTm TWÜm ¨Lrf£úV ùYlTm TWÜRpG]lTÓm. ùYlT¨ûX A§L ®j§VôNmCÚkRôp ùYlTm úYLUôL TWÜm.
ùYlTf NX]m (Convection)
ùYlTm AûPkR êXdáßLs K¬Pj§pCÚkÕ Utù\ôÚ CPj§tÏ úUpúSôd¡SLoYRu êXm ùYlTm TWÜm Øû\ ùYlTfNX]m G]lTÓm. Ck¨Lrf£ §WYlùTôÚhL°Ûm YôÙlùTôÚhL°Ûm¨Lr¡\Õ. ERôWQm: ÅhÓ ÑÓ Ri½oØû\,úUôhPôo Lô¬u á≠e £vPm.
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.11.33
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ùYlTd L§o ÅNp (Radiation)
ùYlTm K¬Pj§p CÚkÕ Utú\ôo CPj§tÏGq®R FPLj§u ER® CpXôUpGXdhúWôþ úUd]¥d úYq (electro-magneticwaves) êXm TWÜ¡u\Õ. CmØû\ ùYlTdL§o ÅNp G]lTÓm. CkR AûXVô]Õ K°AûX Utßm Yôù]ô≠ AûX úTôu\RôÏm.ùXuv êXUôL §Úl×Rp Utßm LiQô¥êXm ©W§T≠jRp, Ck¨LrÜdÏ Gq®RùTôÚs FPLØm úRûY«pûX. ERôWQm.ã¬V²PªÚkÕ éªdÏ ùYlTm TWÜm Øû\.
ùYlTm TWÜRp êuß YûL«pSûPùTß¡u\Õ. AûY ùYlTdLPjRp, ùYlTf NX]m, UtßmùYlTd L§o ÅNp.
ùYlTjRôp ®¬YûPRp (Expansion due toheat)
§Pl ùTôÚs, §WYm ApXÕ YôÙdLû[ùYlTlTÓj§]ôp AûY ®¬YûPÙmUtßm L] A[Ü A§L¬dÏm AúR úTôpAûYLû[ Ï°of£Vôd¡]ôÛm, AûYÑÚeÏm Utßm ARu L] A[Ü Ïû\Ùm.
ERôWQm: CW«púY RiPYô[j§uCûQl©p £±V CûPùY° CÚdÏm. CÕúLôûP LôXj§p HtTÓm ùYlTjRôp,RiPYô[eLs ®¬YûPÙm. CûR N¬ùNnYRtLôLj Rôu CûPùY° AûUdLlThÓs[Õ. CqYôß CûPùY° CpXôUpCÚkRôp RiPYô[eLs ®¬YûPkÕUtßm Yû[kÕ CW«pLs L®rYRtÏLôWQUôÏm.
£X ùTôÚhLû[j R®W GpXô §PlùTôÚhLÞm, §WYeLs Utßm YôÙdÞm®¬YûP¡u\]. §WYl ùTôÚhLs §PlùTôÚhLû[ ®P áÓRXôLÜm, YôÙlùTôÚhLs §WYl ùTôÚhLû[ ®PáÓRXôLÜm ®¬YûP¡u\].
ùTôÕYôL Ri½ûW 00C ØRp 40C YûWùYlTlTÓj§]ôp Ri½¬u L] A[ÜÏû\Ùm. ARu ©\Ï L] A[Ü A§L¬dÏm.40Cþp HtTÓm BRôWl×s°ûV ûUVUôLdùLôiÓ Ri½ÚPu ùRôPo×ûPV Ut\LQd¸ÓLs ùNnVlTÓ¡\Õ.
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.11.33
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¿[l ùTÚdL Gi Utßm ARtÏ ùRôPo×ûPV LQdÏLs Utßm§\]ônÜ T«t£ T«t£ 1.11.34
§iU ùTôÚsL°u ùTÚdLm (Expansion ofsolids)
§iU ùTôÚhLû[ ùYlTlTÓjÕm úTôÕ¸rLiP ùTÚdLeLs HtTÓ¡\Õ.
1 ¿[l ùTÚdLm (Linear expansion)
2 TWl× ùTÚdLm (Superficial expansion)
3 TÚU ùTÚdLm (Cubical expansion)
1 ¿[l ùTÚdLm (Linear expansion)
JÚ §PlùTôÚû[ ãPôdÏm úTôÕ ARu¿[m A§LUôYúR ¿[l ùTÚdLm G]lTÓm.AûY ùTôÚ°u ¿[m A§L¬dÏmùYlT¨ûX Utßm ùTôÚs ùNnVlThPEúXôLm B¡VYtû\ ùTôÚjRÕ.
¿[l ùTÚdL Gi (Co-efficient of linear expan-sion)
JÚ ùTôÚ°u ùYlT ̈ ûXûV 1 ¥¡¬ 0CþdÏEVojÕm úTôÕ ARu ¿[j§p HtTÓmªÏ§lTôh¥tÏm ARu BWmT ¿[j§tÏmEs[ ®¡Rm ¿[l ùTÚdL Gi G]lTÓm. α(BpTô) G] ϱdLlTÓm.
t10C þp §iU ùTôÚ°u ¿[m = l1
t20C þp §iU ùTôÚ°u ¿[m l2
A§L¬jR ùYlT¨ûX = t2 - t10C
A§L¬jR ¿[m = l2 - l1
¿[ ùTÚdL Gi = A§L¬jR ¿[m/BWmT¿[m x ùYlT¨ûX EVoÜ
( )
[ ]ttttlll
ttlll
121
12
121
12
=−−
=
−×−
=
α
α
TWl× ùTÚdL Gi (Co-efficient of superficialexpansion)
JÚ ¥¡¬ 0C ùYlT¨ûX EVoYRôp JÚùTôÚ°u TWlT[®p HtTÓm TWl©uªÏ§dÏm ARu BWmT TWlT[®tÏm Es[®¡Rm TWl× ùTÚdL Gi BÏm. CÕ β(ÀhPô) G] ϱdLlTÓm.
TWl× ùTÚdL Gi = 2 x ¿[l ùTÚdL Gi
β = 2α
3 TÚUl ùTÚdLm (Cubical expansion)
JÚ §iU ùTôÚ°u ùYlT¨ûX EVÚmúTôÕ ARu TÚUu A§LUô¡\Õ. CûRúVTÚUl ùTÚdLm Gu¡ú\ôm.
TÚU ùTÚdL Gi (Co-efficient of cubicalexpansion)
JÚ §iU ùTôÚ°u ùYlT¨ûXûV 1¥¡¬dÏ EVojÕYRôp HtTÓm TÚUuªÏ§dÏm ARu BWmTl TÚUàdÏm Es[®¡Rm TÚUl ùTÚdL Gi G]lTÓm. CÕ γ(LôUô) Guß Ï±dLlTÓ¡\Õ.
TÚU ùTÚdL Gi= 3 x ¿[ ùTÚdL Gi
γ = 3α
ERôWQeLs (Examples)
8 ÁhPo ¿[Øs[ EúXôL Lm© 300Cþ«pCÚkÕ 800CþdÏ ùYlTm EVojRlTÓ¡\Õ. CR]ôp 0.84 ª.Á ¿Þm. ¿[lùTÚdL Gi LiÓ©¥?
BWmT ¿[m (l) = 8 ÁhPo
A§L¬jR ¿[m = 0.84 ª.Á
A§L¬jR ùYlT ¨ûX(t) = 80 - 30 = 500C
A§L¬jR ¿[m = l2-l1 = αl1t
Cߧ ¿[m = l2 = l1(1 + αt)
2 TWl×l ùTÚdLm (Superficial expansion)
JÚ §iU ùTôÚs ãPôdLlTÓm úTôÕARu TWlT[Ü A§LUôYûR TWl×lùTÚdLm Gu¡ú\ôm.
A§L¬jR ¿[m¿[l ùTÚdLGi
=BWmT ¿[m X ùYlT¨ûX
EVoÜ
A§L¬jR ¿[m¿[l ùTÚdLGi (α)
=BWmT ¿[m X ùYlT¨ûX
EVoÜ
508000
0.84
×=
400000
0.84=
= 2.1 x 10-6 /0C
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105
00Cþ ùYlT¨ûX«p JÚ CÚm× TôXm 100ÁhPo. 400C ùYlT¨ûX«p TôXj§u¿[m GqY[Ü CÚdÏm? JÚ ¥¡¬dÏ,¿[l ùTÚdL Gi 12 x 10-6 .
CÚm× TôXj§u BWmT ¿[m = 100 ÁhPo
A§L¬dLlThP ùYlT ¨ûX = 40 - 0 = 400C
A§L¬jR ¿[m¿[l ùTÚdLGi (α)
=BWmT ¿[m X ùYlT¨ûX
EVoÜ
A§L¬jR ¿[m12 X 10-6 =
100 X 40
A§L¬jR ¿[m¿[l ùTÚdLGi (α)
=BWmT ¿[m X ùYlT¨ûX
EVoÜ
100 = L0 (1 + 0.0006)
00C þ«p ¿[m = 99.94 ÁhPo
100 ùN.Á ¿[Øs[ EúXôL Wô¥u (metal-lic rod) A§L¬jR ¿[jûRd LiÓ©¥?ARu ùYlT ¨ûX 25 ¥¡¬ùNu¥¡úW¥≠ÚkÕ 40 ¥¡¬ ùNu¥¡úWPôL A§L¬dLlTÓ¡\Õ. UtßmARu ¿[l ùTÚdÏ Gi 10 x 10-6 / 0C.
BWmT ¿[m = 100 ùN.Á
A§L¬dLlThP ùYlT ¨ûX =40 - 25 = 150C
A§L¬jR ¿[m10 X 10-6 =
100 X 15
A§L¬jR ¿[m¿[l ùTÚdL
Gi (∝) =
BWmT ¿[m X ùYlT¨ûXEVoÜ
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.11.34
A§L¬jR ¿[m = 401001000000
12××
= 0.048 ÁhPo
40 ¥¡¬ ùNu¥¡úWh¥p CÚm× TôXm =
= 100 + 0.048 = 100.048 ÁhPo
300C þ«p EúXôL Lm©«u ¿[m 100 ùN.ÁUtßm 1000Cþ«p ARu ¿[m 100.14 ùN.Á.¿[l ùTÚdL Gi Utßm 00C þp Lm©«u¿[jûRÙm LiÓ©¥?
300 ùNu¥¡úW¥p BWmT ¿[m = 100 ùN.Á
1000 ùNu¥¡úW¥p Cߧ ¿[m = 100 .14ùN.Á
A§L¬jR ¿[m = 0.14 ùN.Á
A§L¬jR ùYlT¨ûX = 100 þ -30 = 700C
00C þ«p ¿[jûRd LiÓ©¥dL
L1 = L0 (1 + αt)
100 = L0 (1 + 2 x 10-5 x 30)
A§L¬jR ¿[m¿[l ùTÚdLGi (α)
=BWmT ¿[m X ùYlT¨ûX
EVoÜ
¿[l ùTÚdÏ Gi (α) = 10 x 10-6/0C
A§L¬dLlThP ¿[m = 10 x 10-6 x 100 x 15
A§L¬dLlThP ¿[m = 0.015 ùN.Á
20 ¥¡¬ ùNu¥¡úW¥p EúXôL Õi¥u¿[m 2.5 ÁhPo. ARu ¿[l ùTÚdÏ Gi10.4 x 10-6 ¥¡¬ ùNu¥¡úWh Gu\ôp, AÕ¿[YôhPj§p 0.54 ª.Á ¿[m A§L¬jRôpARu ùYlT ¨ûXûVd LiÓ©¥?
BWmT ¿[m = 2.5 ÁhPo
= 2500ª.Á
A§L¬jR ¿[m = 0.54 ª.Á
BWmT ùYlT ¨ûX = 200C
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106
0.5410.4 X 10-6 =
2500 X A§L¬jR ùYlT ¨ûX
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.11.34
Cߧ ùYlT¨ûX = 20 + 20.77
= 40.770C
§\]ônÜ T«t£ (Assignment)
¿[l ùTÚdL Gi (Co-efficient of linear expan-sion)
1 100 Á ¿[Øs[ Lm© 200C -p CÚkÕ 1000C-dÏ ùYlTlTÓjÕm ùTôÝÕ AdLm©100.14 Á ¿[j§tÏ ®¬YûP¡\Õ G²pLm©«u ¿[l ùTÚdL GiûQdLiÓ©¥.?
2 3.6 Á ¿[Øs[ Lm© 1200C ùYlT¨ûXdÏEVojRlTÓ¡\Õ. Lm©«u ¿[lùTÚdLGi 0.00024/0C G²pA§L¬jR Lm©«u¿[m GqY[Ü?
3 6 Á ¿[Øs[ Lm©ûV 1200C ùYlT¨ûXdÏEVoj§]ôp A§L¬jR Lm©«u ¿[mGqY[Ü? Lm©«u ¿[l ùTÚdL Gi10x10-6/0C.
4 100 ùNÁ ¿[Øs[ Lm©ûV 400CùYlT¨ûX«p CÚkÕ 900C ùYlT¨ûXdÏEVoj§]ôp Lm©«u ¿[m GqY[ÜA§L¬jÕ CÚdÏm. CÚm©u ¿[l ùTÚdLGi 10x10-6/0C.
5 150C -p ûUdúWô ÁhP¬u Ã¥e¨ûXlTÓjRlThÓ Es[Õ (standardised)AÕ 350C -p 20.20 ªÁ -VôL JÚ A[ûYLôh¥]ôp, EiûUVô] Ã¥e GqY[Ü?
ûUdúWô ÁhP¬u ¿[lùTÚdL Gi11 x 10-6/0C.
2500 X 10.4 X 10-6
0.54A§L¬jR ùYlT
¨ûX
=
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107
ùYlT CZl× Utßm ùYlT Ht× LQdÏLs Utßm §\]ônÜ T«t£T«t£ 1.11.35
LXl× ùYlT CVp (Mixing of heat) m1 = ØRp ùTôÚ°u ¨û\
s1 = ØRp ùTôÚ°u ùYlT Gi
m2 = CWiPôYÕ ùTôÚ°u ̈ û\
s2 = CWiPôYÕ ùTôÚ°u ùYlT Gi
tm = LXûY«u ùYlT ¨ûX
m = ¨û\
Q = ùYlT A[Ü
δt/Δt = ùYlT¨ûX úYßTôÓ
tm = LXûY«u ùYlT ¨ûX
ùYlTj§u AXÏ (Unit of amount of heat)
ùYlTj§u Y¯ ̈ ûX AXÏLs (derived unit) S.I.Øû\«p ùYlTj§u AXÏ _øp BÏm.
ùYlT Gi (Specific heat)
1 ¡úXô ¡Wôm ¨û\Ùs[ JÚ ùTôÚ°uùYlT ¨ûXûV 1 ¥¡¬ EVojÕYRtÏúRûYVô] ùYlTm AlùTôÚ°u ùYlTGi G]lTÓm. CRu ϱÂÓ C BÏm.
úRûYlTÓm ùYlTm (A)ùYlTj§uùUdLô²dLp NUu = 4186 _øpLs
= 4.2 kj/kg°C.
JÚ ùTôÚ°u ùYlT¨ûXûVEVojÕYRtÏ úRûYVô] ùYlTm (Quan-tity of heat needed for a substance to rise the tem-perature
JÚ ¡úXô ¡Wôm ¨û\Ùs[ JÚ ùTôÚ°uùYlT ¨ûXûV 1°CþdÏ EVojÕYRtÏúRûYVô] ùYlTm, ùTôÚ°u ùYlT Gi‘s’ G]lTÓm. ‘m’ ¡úXô¡Wôm ¨û\Ùs[ JÚùTôÚû[ ùYlTlTÓj§ ‘t’ Gu\ ARu JÚùYlT¨ûX ®j§VôNm A±V
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108
úRûYVô] ùYlT A[Ü = m x s x Δt
BûLVôp Q = m x s x Δt
LXûY (Mixing)
ùYlT ¨ûX Uôt\eLs ¨LÝm ùTôÝÕùYlT Uôt\ ̈ LrÜm SûPùTß¡\Õ. EVokRùYlT ̈ ûX«p Es[ JÚ §iUl ùTôÚû[Ïû\kR ùYlT ¨ûX«p JÚ ùTôÚú[ôÓúNojÕ LXdÏm úTôÕ ùYlT ¨ûX A§LmEs[ ùTôÚ°≠ÚkÕ Ïû\kR ùYlT¨ûXùTôÚÞdÏ ùYlTm LPjRlTÓ¡\Õ. CÕCWi¥u ùYlT ̈ ûXÙm NU¨ûXdÏ YÚmYûW ̈ Lr¡\Õ.
EVokR ùYlT ¨ûX«p Es[ ùTôÚsCZdÏm ùYlTm =
Ïû\kR ùYlT ¨ûX«p Es[ ùTôÚsAûPÙm ùYlT Ht×. Utßm ùTôÚ°uTôLj§p HtTÓm ùUôjR ùYlT ¨ûX =
LXûY«u ùYlTj ùRôûL.
ùYlTl ùTôÚs CZdÏm ùYlTm =Ï°of£Vô] ùTôÚs ùTßm ùYlTHt×.
S Gu\ Tϧ«p HtTÓm ùUôjRùYlTm = LXûY«u ùUôjRùYlTm.
m1 x s1 x t1 + m2 x s2 x t2 = (m1s1 + m2s2)tm.
ERôWQm (Example)
Ï°dÏm ùRôh¥«p 15°Cþp 40 ≠hPoRi½o Es[Õ þ A§p 60°Cþp Es[ 80≠hPo Ri½o Ft\lTÓ¡\Õ. CkR Ri½oLXûY«u ùYlT ¨ûX GqY[Ü?
m1 x s1 x t1 + m2 x s2 x t2 = (m1s1 + m2s2)tm.
ERôWQeLs (Examples)
JÚ ùLôsLXj§p 25 ¡úXô Ri½oEs[Õ. ùLôsLXm Utßm Ri½¬uùYlT¨ûX 250C. Ri½ûW ùLô§¨ûXdÏ ùLôiÓ YW úRûYlTÓm ùYlT¨ûXûVd LiÓ©¥. ùLôsLXj§uùYlTf NU ¿o = 1 ¡úXô
Ri½¬u ̈ û\ (m) = 25 ¡úXô
Ri½o Utßm ùLôsLXj§uBWmT ùYlT ¨ûX = 250C
Ri½o Utßm ùLôsLXj§uCߧ ùYlT ¨ûX = 1000C
A§L¬dLlThP ùYlT ¨ûX (t) = 100 - 25
= 750C
ùYlTf NU¿o (m s) = 1 ¡úXô
ùLôsLXj§tÏ úRûYVô]ùYlTm = m s t
= 25 x 1 x 75
= 1875 ¡úXô LúXô¬ (K.cal)
Required amount of heat to container = m s t= 1 x 75
= 75 K.cal.
úRûYVô] ùUôjR ùYlTm = 1875 + 75
= 1950 ¡úXô LúXô¬ K.cal.
300 ¡Wôm Ri½¬u ùYlT ¨ûX 250CUtßm 200 ¡Wôm Ri½¬u ùYlT ̈ ûX850C. CWiÓm Ju\ôL LXdLlTÓ¡\Õ.CqYôß Ri½ûW LXkR ©\Ï ARuCߧ ùYlT¨ûXûVd LiÓ©¥. C§pùYlT CZl× HÕm CpûX.
i Ri½¬u GûP = 300 ¡Wôm
BWmT ùYlT ¨ûX = 250C
Cߧ ùYlT ¨ûX = ‘X’ G] ùLôsL
ùYlT Ht× = x - 250C
ii Ri½¬u ̈ û\ = 200 ¡Wôm
BWmT ùYlT ¨ûX = 850C
ùYlT CZl× = 850C - x
300 ¡Wôm Ri½¬uùYlT Ht× = m s t
= 300 x 1 x (x - 25)
= 300 x -7500 LúXô¬ (cal).
200 ¡Wôm Ri½¬uùYlT CZl× = m s t
= 200 x 1 x (85 - x)
= 17000 - 200 x LúXô¬ (cal)
ùYlT Ht× = ùYlT CZl×
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109
300 x -7500 = 17000 - 200 x
300 x + 200 x = 17000 + 7500
500 x= 24500
x= 24500 = 490C
500
Cߧ ùYlT ¨ûX = 490C
200 ¡Wôm ̈ û\Ùs[ 910C ùYlT ̈ ûX«pEs[ NôRôWQ El× 250 ¡Wôm ̈ û\ÙPu130C ùYlT ̈ ûX«p Es[ PoTuûP²pÖûZdLlTÓ¡\Õ. Cߧ ùYlT ¨ûX160C PoTuûPu B«≠u ÑV ùYlTHt×j §\u0.428 G²p, NôRôWQ El©uÑV ùYlT Ht×j §\û] LiÓ©¥.
El©u ̈ û\ (m) = 20 ¡Wôm
BWmT ùYlT ¨ûX (t) = 910C
PoTuûP²u ̈ û\ (m) = 250 ¡Wôm
BWmT ùYlT ¨ûX (t) = 130C
PoTuûP²u ÑVùYlTm (s) = 0.428
LXûY«u CߧùYlT¨ûX = 160C
PoTuûP²u ùYlTHt× (Q) = m s t
= 250 x 0.428 x (16-13)
= 250 x 0.428 x 3
= 321 LúXô¬
NôRôWQ El× CZkRùYlTm (Q) = m s t
= 20 x s x (91-16)
= 20 x s x 75
= 1500 s. LúXô¬
ùYlT CZl× = ùYlT Ht×
1500 s = 321
NôRôWQ El©u ÑV ùYlTHt×j §\u (s) = 0.214
JÚ ùNm× LúXô¬ ÁhP¬p, 80 ¡Wôm¨û\Ùs[ Ri½o 200C þp Es[Õ.LúXô¬ ÁhP¬u ¿o NU¨ûX 20 ¡Wôm.AjÕPu Ri½¬u ùYlT ̈ ûX 400C þpEs[ 100 ¡Wôm ¨û\Ùs[ ¿ÚPuCWiûPÙm LXkR ©\Ï ARu ùYlT¨ûX Gu]?
LúXô¬ ÁhP¬p Ri½¬u¨û\ = 80 ¡Wôm
ùYlT¨ûX = 200CLXûY«u Cߧ ùYlT¨ûX = ‘x’ G]d ùLôsL
Ri½¬u EVojRlThPùYlT¨ûX = x - 20
LúXô¬ ÁhP¬u ¿oNU¨ûX = 20 ¡Wôm
úNodLlThP Ri½¬u¨û\ = 100 ¡Wôm
ùYlT¨ûX = 400C
ùYlT CZl× = 40 - x
ùYlT Ht×
LúXô¬ ÁhP¬p ¿o HtßdùLôiP ùYlTm = m s t
= 80 x 1 x (x - 20)
= 80 x -1600
LúXô¬ ÁhPo HtßdùLôiP ùYlTm = m s t
= 20 x (x - 20)= 20 x (-400)
ùYlT CZl×
¿o úNodLlThPRôp HtThPùYlT CZl× = m s t
= 100 x 1 x (40 - x)
= 4000 - 100x
ùYlT Ht× = ùYlT CZl×
80 x -1600 + 20 x -400= 4000 - 100x
100 x -2000 = 4000 - 100x 100x +100x = 4000 + 2000 200x = 6000 x = 6000/ 200
= 30
Cߧ ùYlT¨ûX = 300C
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.11.35
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15 ¡Wôm ¨û\Ùs[ Iv Lh¥ -80Cþ«pEs[ûR ùLô§dL úRûYlTÓmùYlTjûRd LiÓ©¥? T²dLh¥«uEs Uû\ ùYlTm =336_øp /¡Wôm.¿Wô®«u Es Uû\ ùYlTm = 2268_øp/¡Wôm. IvLh¥«u ÑV ùYlT Ht×j§\u 0.5
Iv¡ë©u ùYlTm
-80CþpCÚkÕ 00C = mct kJ= m x s x 4.2 x t kJ
= 0.015 x 0.5 x 4.2 x 8 kJ
= 0.252 kJ
00C þ«p Es[ Iv Lh¥ûV00C Ri½WôL Uôt\ = m x h s f kJ
= 0.015 x 336 kJ
= 5.04 kJ
00C «p Es[ Ri½ûW1000C þdÏ EVojÕRp = m c t kJ
= 0.015 x 4.2 x 100 kJ
= 6.3 kJ
1000C «p Es[ Ri½ûW1000C þdÏ ¿Wô®VôL Uôt\Üm = m x hsfg kJ
= 0.015 x 2268 kJ
= 34.02 kJ
ùUôjR ùYlTm Q
= 0.252 + 5.04 + 6.3 + 34.02 kJ
®ûP = 45.612 kJ
§\]ônÜ T«t£ (Assignment)Mixing of Heat
1 m = 120 ≠hPo
t 1 = 20°Ct 2 = 85°Cs = 4.2Q = ______ kj
2 m 1 =80 ≠hPo Ri½oó
m 2 =40 ≠hPo Ri½o
t 1 = 10°Ct 2 = 70°Ct m = ______ °C
3 m1 = 25 ≠hPo Ri½oó
t 1 = 12°Ct 2 = 70°Ct m = 33.75°Cm 2 = ______≠hPo
4 m 1 = 100 ¡.Ri½oót 1 = 12°Cm 2 = 50 ¡.G@Ït 2 = 600°C
Ri½¬u ùYlT EVoÜ =_____°C ≠hPo Ri½oó
5 m1 = 250 ≠hPo Ri½oó
m2 = 150 ¡.G@Ï
t1 = 15°Ctm = 70°Ct2 = ______ °C
6 m1 = 20 ≠hPoùU£u B«p
m2 = 30 ¡.G@Ï
t2 = 160°Ctm = 60°CGiùQn - u
APoj§
t1 = ______ °C = 0.91 3cm
gr
7 m1 = 10 ≠hPo
CK g
kj 4.2
1S
°=
CK g
kj 0.46
2S
°=
m2 = 0.5 kgt1 = 18°Ct2 = 780°C
Ri½¬u ùYlT EVoÜ =___°C
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8 m1 = 60 ¡.Ri½oó
m = 70 LúXô¬ÁhPo ¡Wôªpm2 = 80 EúXôLm ¡Wôªp
t1 = 200Ct2 = 95 0 Ctm = 250Cs = 0.2s1 = 1s2 =_____
9 m1 = 250 B«p ¡Wôªp
t1 = 15oCm2 = 150 ©jRû[
¡Wôªp
t2 = 900Ctm = 25°Cs2 = 0.09 Ri½o
LúXô¬ ÁhPoNU¨ûX = 3 ¡Wôms1 = ______ ¡Wôm
ùYlT CZl× Utßm ùYlT Ht× (Heat lossand heat gain)
1 85.5 ¡Wôm UQûX 200C -«≠ÚkÕ 350C -dÏEVokR úRûYVô] ùYlT A[®û]LiÓ©¥. UQ≠u ùYlT Gi = 0.1.
2 11 ¡úXô/¨ªPm JÓm A[®p Es[ ¿o120C A[®tÏ EVojRlTÓ¡\Õ. G²p 1U¦ úSWj§p GqY[Ü ùYlTmCZdLlTh¥ÚdÏm G] LiÓ©¥.
3 170 ¡Wôm ¨û\Ùs[ ùTôÚû[ 500C -«≠ÚkÕ 800C -dÏ EVojR 510 LúXô¬úRûYlTÓ¡\Õ G²p ùYlT GiûQdLiÓ©¥.
4 500 ¡Wôm ̈ û\Ùs[ EúXôLjÕiÓ 3000CùYlT¨ûX«p 5 ¡úXô GûPÙs[ ¿¬p®Ý¡\Õ, AlùTôÝÕ ARu ùYlTm 300C- -≠ÚkÕ 750C BL EVÚ¡\Õ G²p,EúXôLjÕi¥u ùYlT GiûQLiÓ©¥ (ùYlT CZl× HÕm CpûX).
5 250C ̈ ûX«p Es[ 300 ¡Wôm Ri½ÚPu850C ¨ûX«p Es[ 200 ¡Wôm Ri½oLXdLlTÓ¡\Õ G²p, CkRd LXûY«uCߧ ùYlT¨ûXûVd LôiL. (ùYlTmHÕm ùY°úV\®pûX G]d ùLôsL).
6 400C ¨ûX«p 100 ¡Wôm GûPÙs[Ri½ÚPu 200C ̈ ûX«p Es[ 80 ¡WômGûPÙs[ Ri½o LXdLlTÓ¡\Õ G²p,CkRd LXûY«u ùUôjRùYlT¨ûX«û]d LôiL. (LúXô¬ÁhP¬u Ri¦o NU¨ûX = 20 ¡Wôm).
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AÝjRj§u LÚjÕÚ Utßm TpúYß Øû\L°p ARu AXÏLsT«t£ 1.11.36
AÝjRm (Pressure)F - ®ûN, EkÕRp
P - AÝjRm
AÝjRj§u LÚjÕÚ
JÚ ®ûN JÚ ùTôÚ°u AXÏ TWl©u ÁÕùNVpTÓm ®û]úV AÝjRm G]lTÓm.
AÝjRm ‘P’ = ®ûN (A) EkÕRp F AXÏTWl× BÏm. (TPm 1)
A - ®ûN ùNVpTÓm R[j§u TWl×
ERôWQm
JÚ §WYm 2Á2 TWl©u ÁÕ 100 N ®ûNùNÛj§]ôp ARu AÝjRm Gu]GuTûRd LiÓ©¥?
®ûN = 100N
TWl× = 2m2
AÝjRm = ?
= 50 N/Á2
§WYj§u ̈ û\Üß ùYlT¨ûX (§WYm/B®VôRp) (Saturation temperature of a fluid (liq-uid/vapour)§WYm, B® ¨ûXdÏ Uôßm ùTôÝÕ JÚϱl©hP AÝjRj§p Es[ ùYlT¨ûXBÏm. CeÏ AÝjRm AúR Uô\ô ¨ûX«pûYdLlTÓm ùTôÝÕ, ùYlT ¿dL ùNnØû\B®ûV §WYUôL AúR ¨ûXVô]ùYlT¨ûX«p Uôtßm. CÕ §WYj§u¨û\Üß ¨ûX G] AûZdLlTÓ¡\Õ(§WYm/B®).
AÝjRj§u AXÏ ̈ /Á2 = 1 ̈ /Á2 = 1 TôvLp
CkR AXÏ ªLÜm £±VÕ. (1 ùNÁ TWl©pJÚ D«]ôp HtTÓm AÝjRm). G]úYAÝjRj§tÏ “Tôo ” (bar) AXLôLA±ØLlTÓjRlThPÕ.
1 Tôo = 105 TôvLp
1 Tôo = 1000 ªp≠ Tôo. ( S.I A[Ü Øû\«pAÝjRj§tÏ TôvLp (Pa) Utßm ùUh¬dØû\«p “Tôo” BÏm.
AÝjRj§u RuûULs (Properties of pressure)
1 BZm A§L¬dL A§L¬dL §WYj§uAÝjRm A§L¬dÏm.
2 JÚ Ï±l©hP ×s°«p §WYj§uAPoj§ûV ùTôßjÕ AÝjRmA§L¬dÏm.
3 §WYm ¨ûXVôL CÚdÏm ùTôÝÕ JÚϱl©hP ×s°«p AÝjRm GpXô§ûNL°Ûm JúW A[®p CÚdÏm.
4 JÚ ×s°«p §WYj§p úUp úSôd¡VAÝjRØm, ¸r úSôd¡V AÝjRØm NUA[®p CÚdÏm.
§WYj§u ¨û\Üß AÝjRm (Saturationpressure of a fluid)JÚ Ï±l©hP ùYlT¨ûX«p áhÓm (A)Ïû\dÏm ùYlTm, AkR §WYj§uCVp©Vp RuûUûV Uôtß¡\Õ. ùLôÓdLlTÓm ¨ûXVô] AÝjRúU §WYj§u¨û\Üß AÝjRm Guß A±VlTÓ¡\Õ.
¡¬h¥Lp ùYlT¨ûX Utßm AÝjRm(Critical temperature and pressure)GpXô §WYeLÞdÏm (§WYm/YôÙ )A§LThN ùYlT¨ûX Utßm AÝjRmEs[Õ. ARtÏd ¸úZ ùYlTjûR¿d¡]ôúXô ApXÕ áÓRp ùNnRôúXôARu CVp©Vp ¨ûX Uô±®Óm.ùYlT¨ûX/AÝjR¨ûX, ̈ û\Üß ̈ ûXûVRôi¥]ôp, B®ûV Ï°o®jÕ §WYUôLUôt\ CVXôÕ. GkR B® Ï°o®jRp êXm§WYUôL Uôt\ Ø¥VôúRô, AûR YôÙ GußAûZd¡ú\ôm.
úUp¨ûX ùYlTm ùNnVlThP B® (Su-per heated vapour)JÚ B®«u ùYlT¨ûXûV ARu ̈ û\ÜßùYlT¨ûXdÏ úUp ùYlTlTÓjÕmØû\dÏ úUp¨ûX ùYlTm ùNnVlThPB® Guß ùTVo, CÕ Ï±l©hPAÝjRj§p CÚdÏm
AÝjRm (Pressure)
©¬h¥x TÜih/AeÏXm2 lb/in2
FPS AXÏùUh¬d ¡Wôm/ùNÁ2 g/cm2
AXÏ CGSMKS ¡úXô ¡Wôm/ kg/m2
ÁhPo2
NoúYRN ¨ëhPuv/ N/m2
ÑtßLs SI ÁhPo2
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ùYlT LPjÕm §\u Utßm Lôl× ùTôÚsLs T«t£ 1.12.37
LXl× ùTôÚsLs (Insulating materials)
ùYlTm A§L ùYlT¨ûX«≠ÚkÕ Ïû\kRùYlT¨ûXdÏ ùNpÛm. ùYlTm, ùYlTL§oÅNp , ùYlTdLPjRp, ùYlTfNX]mB¡V Øû\L°p ÑYt±u FPôLúYô, LRÜ,úUtáûW Utßm Ï°o TR]m ùNnVlThPAû\«u LiQô¥dLRÜL°u êXUôLúYôùNpÛm.
CkR YûL ùYlTdLPjRûX RÓdÏmùTôÚsLú[ Lôl×l ùTôÚsLs (insulatingmaterials) Guß AûZdLlTÓ¡u\].
Lôl× ùTôÚsL°u RuûULs (Propertiesof insulating materials)
- ªLd Ïû\kR LPjRp RuûU
- ¾«û] RÓdÏm RuûU
- Ïû\kR A[Ü DWlTRjûR E±gÑmRuûU
- UQªuûU
- úYlTo ùToªVô©≠h¥ (Vapour permeability)
- CXÏYô] GûP
Lôl×l ùTôÚsLû[ úRoÜ ùNnRp(Selection of insulating material)
JÚ N¬Vô] Lôl×l ùTôÚû[ úRoÜùNnYRtÏ ¸rLiP LôW¦Ls ªLAY£VUô] Ju\ôÏm.
Ïû\kR ùYlTdLPjRp RuûU (Lowthermal conductivity)
ùYlTdLPjRp Esú[ ¨LÝm ùTôÝÕARôYÕ ùYlTm ºWôL LPkÕ ùNpÛmùTôÝÕ AkR ùYlT¨ûX ÅQôLôUpØÝûUVôL TVuTÓjÕYRtÏ Ïû\kRùYlTdLPjRp RuûUÙûPV ùTôÚsAûRf Ñt± úRûYlTÓ¡\Õ. AûYVôY]
- ¾«û]j RÓdÏm RuûU
- CVk§W®Vp Eߧj RuûU
- Ïû\kR A[Ü ¿o B®ûV E±gÑm RuûU
- AûUlTRtÏ G°RôL CÚlTÕ
- ®ûX (Cost)
- ûLVôsYRtÏ G°RôL CÚlTÕ
- Ïû\kR ®ûX
Lôl× ùTôÚsL°u YûLLs (Types ofinsulating materials)
¡[ôvÜp, PUF , RdûL AhûP,ùRoúUôúLôp, Lôl× RLÓ, @ûTTo ¡[ôv.
Lôl× ùTôÚsL°u YûLLs (Types ofinsulating materials)
A¥lTûP YûL«Xô] Lôl× ùTôÚsLsGpXôm ùNVtûL Sôo CûZ«]ôúXô (A)ùNpíXo ùTôÚsL°]ôúXô RVô¬dLlTh¥ÚdÏm. ERôWQm - ¡Xôv Ep, vXôdEp -«]ôp ùNnVlThP ÀeLôuùTôÚsLs, BvùTvPôv Utßm TX,CVtûL CûZ ùTôÚsLs, RdûL, TgÑ, WlToÖûW, UWjçs, ùSp Eª, Tô≠ vùP¬u,Tô≠ëìj¾u, ©ú]ôjùRom Utßm TX.TpúYß Lôl× TVu Tôh¥tLô] YûLUtßm ¡ûPdÏm Y¥YeLs ¸rYÚUôß.
¡Xôv Ep (Glass wool)
CÕ Tϧ §Pm, ùW£u TôiPh vXôl (A)RLÓL[ôL ùYqúYß APoj§L°p¡ûPd¡\Õ. C§p A§L APoj§ùLôiPûY RôeÏjRuûU A§LmEûPVRôLÜm Utßm Ïû\kR LPj§pEûPVRôLÜm B]ôp B®VôRûXAàU§dÏm YûL«Ûm CÚdÏm. úUpêÓYRtÏ YN§VôL CÕ @Tô«p (foil) EPu¡ûPd¡\Õ.
RdûL (Cork)
CÕ AÝjRlThÓ §PUô] ©[ôd BLúUôpÓ (mould) ùNnVlTh¥ÚdÏm. CÕCúXNôL CÚkRôÛm §PUô]Õ, CûRG°RôL WmTj§u êXm ùYhPXôm. CÕ ¿oùNpYûR RÓdÏm B]ôp A§L A[Ü ¿oB®VôLf ùNpYûR AàU§dÏm.
GdvùTiPh Tô≠vùP¬u(ùRoúUôúLôp ) Expanded polystyrene(Thermocole)
CÕ EߧVô] TXûLVôL, ÕLsL[ôL, ÏZôn/Yû[Yô] TWl×Lû[ EûPV Y¥Yj§púUôpÓ ùNnÙm YûL«p ¡ûPd¡\Õ. CûRG°RôL WmTj§u êXm ùYhPXôm.úXNô]Õ Utßm Ïû\kR A[ÜùYlTdLPjRûX AàU§dÏm.
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Tô≠ë¬j§u (Polyurethane)
CÕ §iûUVô] TXûLVôL, ùS°Yô]TXûLVôL ¡ûPd¡\Õ. §WYeLs CkRTWl×L°u ÁÕ ùR°dLlThÓ AûYÖûWYôL Uôß¡\Õ. CqYûL TXûLLsTpúYß LhÓUô] CPeL°pTVuTÓjRlTÓ¡u\].
UWfºYp/UWjçs (Wood shaving/Saw dust)
CÕ G°RôL AUokÕ AûUYRtÏ ùT¬VA[®Xô] RôeÏ ùTh¥LsúRûYlTÓ¡u\]. CÕ Su\ôL LPjÕmUtßm DWjRuûUûV E±gÑm.
©ú]ôjùRom (Phenotherm)
CÕ TXØLTWl×Lû[ EûPV TXûLVôLÜmUtßm, ûTl ùNd`uL°ÛmTVuTÓjRlTÓ¡\Õ. CûR WmTjûRdùLôiÓ G°RôL ùYhPXôm.
Lôl×ùTôÚsLs Utßm RuûULs/®YWd ϱl×Ls (Insulating materials and prop-erties/specifications)
Ï°oTR]m Utßm Lôtû\ TRlTÓjÕmÕû\«p TXYûLVô] Lôl× ùTôÚsLsTVuTÓjRlTÓ¡\Õ. Sm Ri½oùRôh¥L°p JÚ £X YûLLú[ETúVôLj§p CÚkR].
Cuû\V LôXLhPj§p ¸rYÚm Lôl×ùTôÚsLú[ TWYXôL TVuTÓjRlTÓ¡u\].
- ùRoúUôúLôp
- ¡XôvÜp/Rôo @ùTph
- T@l (Puf)
- @ûTTo ¡Xôv
ùRoúUôúLôp (Thermocole)
CÕ ùTôÕYô] TVuTôh¥p Es[ Lôl×ùTôÚ[ôÏm. CÕ Ïû\kR Utßm A§LAPoj§ YûLL°p ¡ûPd¡\Õ. CRu R¥Uu0.25" ≠ÚkÕ 5" YûW úYßTÓ¡\Õ.
úRûYdÏ HtT TpúYß Y¥YeL°p(moulded shapes) BL ¡ûPd¡\Õ.
ùRoúUôúLôp ùTôÕYôL Ïû\kR A[úYùYlTjûRdLPjÕm (ÏQm ) , CRuLôWQUôL ùYlTm Esú[ YÚYÕRÓdLlTÓ¡\Õ. CÕ Ïû\kR Utßm A§LAPoj§ Lôl× ùTôÚÞdÏ HtT úYßTÓm.
CûR G°RôL NôRôWQ Lj§«]ôpúRûYlThP Y¥Yj§tÏ ùYh¥dùLôs[Xôm. ùRoúUôúLôp Ï°of£/ùYlTm B¡V CWiûPÙm ¿iP úSWmRôeÏm Nd§ EûPVÕ.
Lôl× ùTôÚ°u 'K' LôW¦ ('K' factor)¸rLiPYôß CÚdÏm (ùRoúUôúLôp).
ùRoúUôúLôp (Thermocole)
-0.20 btu/hr Ft2 deg.f°/inch
@ûTTo¡Xôv (Fibreglass)
JÚ YûL Lôl× ùTôÚs, L²UlùTôÚsL[ôp RVô¬dLlTÓ¡\Õ (UQp,úPôúXôûUh, ÑiQôm×d Lp). ùYlT¨ûXúYßTôh¥]ôp @ûTTo¡Xôv Lôl×ùTôÚs ÑÚeÏY§pûX.
CkR YûL Lôl× ùTôÚsLs EVokR ùYlT¨ûXL°Ûm TVuTÓjRlTÓ¡u\]. (450°C(A) 842°F).
Aû\ ãr¨ûX«p Es[LôtßUiPj§≠ÚkÕ @ûTTo¡Xôv DWjûRE±gNôÕ.
¡[ôvÜp (Glass wool)
¡[ôvÜp A§L ùU≠Rô] AÓd¡p Es[ùTôÚ[ôÏm, ùUuûUVô]Õ (EQÚmùTôÝÕ). CÕ TpúYß A[ÜL°p (R¥Uu0.5" ≠ÚkÕ 2.5" YûW) ¡ûPd¡\Õ. CÕùYsû[, UgNs YiQeL°p çsùNnVlThP LiQô¥j ÕLsLú[ôÓLXkÕ CÚdÏm.
¡[ôvÜp -I ûLVôsYÕ BTjRô]ÕUtßm ¾eÏ®û[®dLd á¥VÕ. (êfÑdLôt±u êXm ÑYô£dÏm ùTôÝÕ )GlùTôÝÕm ¡[ôvÜp -I ûLÙûW,Li¦tÏ TôÕLôl× LiQô¥ B¡VYtû\úYûX ùNnÙm ùTôÝÕ TôÕLôl×d LôWQmLÚ§ A¦V úYiÓm. CÕ TpúYßAPoj§L°p ¡ûPd¡\Õ.
¡[ôvÜp -Ls CWiÓ YûL«pETúVôLlTÓ¡u\]. JÚ YûL ¡XôvÜpÏû\kR ùYlT¨ûX EûPV Ï°oTR]m/Lôtß TRlTÓjÕm TVuTôh¥tLôLETúVôLlTÓjRlTÓ¡u\]. Utù\ôÚ YûLùLô§ LXuL°p (ùYlTd Lôl©tLôL)TVuTÓjRlTÓ¡u\].
Lôl× ùTôÚÞdLô] 'K' LôW¦Ls ('K' factor)
¡XôvÜp: 0.230-.27 Btu/Hr ft2 deg. F°/inch.
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.12.37
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T@l (Puf)Cuù]ôÚ YûL«p Ï°okR Ri½oùLôÓdÏm ùU£²p Es[ GúYôlTúWhPoùRôh¥dÏ ùY°l×\m (evaporator tank's)TVuTÓjRlTÓm Lôl×ùTôÚs BÏm.
CkR YûL Lôl×LÞdÏ CWiÓCWNôV]eLs TVuTÓjRlTÓ¡u\].(IúNôûNVû]Ó -R11). CûY CWiÓm§WY¨ûX«p LiQô¥ Ïl©L°p (Ïû\kRA[Ü ùLôs[[®tÏ) Utßm úLuL°p(A§L A[Ü ùLôs[[®tÏ) ¡ûPd¡u\].
CkR CWiÓ §WYeLÞm (CWNôV]eLs)GlùTôÝÕm Ï°okR ¨ûX«úXúVûYdLlTh¥ÚdL úYiÓm, CûYCWiûPÙm JÚ Tôj§Wj§p (ùLôsLX²p)úNojÕ Su\ôLd LXd¡]ôp AÕ ÖûWVôLUôßm (BWmTj§p ùU≠RôL Es[ÕR¥U]ôL Uô± Cߧ«p L¥]Uô¡®Óm)(ùLôsLXàPu Jh¥d ùLôiÓ ®Óm).
ãZlThP (A) êPlThP ùLôsLX²pLôtß ×Ïm YûL«p GkR JÚ CûPùY°CpXôRYôß TôojÕd ùLôs[ úYiÓm.CÕ ÖûWVôL A§L APoj§«pTPok§ÚdÏm Utßm ùY°l×\m JÝeLt\(finish) ùLôi¥ÚdÏm.
T@l (Puf materials) Lôl×Ls TWYXôLRVô¬lTô[oL[ôp TVuTÓjRlTÓYRuLôWQm AÕ ùYlT ¨ûXûV ¿iPúSWj§tÏ RdLûYlTúRVôÏm.
CûRl TVuTÓjÕY§p Es[ AàáXUt\RuûU Gu]ùY²p CkR ùNnØû\«pCWiÓ WNôV]eLû[ LXkRÜPuEP]¥VôL Su\ôL LXd¡®hÓGúYôlTúWhPo Lô«p úUp (A )GúYôlTúWhPo tank -tÏ ùY°l×\mÏû\kR U¦jÕ°L°p Ft±®P úYiÓm.LôXm LPkÕ ®hPôp §WYd LXûY §PUô¡AkR ùLôsLXú] TV]tßl úTôn®ÓmãZp HtThÓ®Óm.
CkR §WYd LûWNûX FtßYRtÏ Øu]ôpGúYôlTúWhPo (tank) ØÝûUVôL UWm/G@ÏúTôo¥]ôp úRûYVô] CûP ùY°®hÓCßd¡ ûYdLlTP úYiÓm.
Pd¥tÏ Lôl× AûUdÏm Øû\ (Methodof laying duct insulation)
Pd¥p DWlTRm ReÏYRtLô] A±Ï±CpûXùV²p, ¡XôvÜp -I TVuTÓjRXôm.Hù]²p CÕ ¾ûVjRÓdÏm Utßm
ùTôÚ[ôRôW A¥lTûP«p £dL]Uô]Õ.G²àm DWlTRm ReÏm ThNj§p¡XôvÜp TVuTÓjÕm ùTôÝÕ £\l×LY]m GÓjÕd ùLôs[ úYiÓm. ØR≠pPdûP Ñt± Ft\lTP úYiÓm (A) RôoTô«]ôp êP úYiÓm. ARu úUp¡XôvÜp JhÓUôß ùNnV úYiÓm. ©\ÏLôl×l ùTôÚû[ Tô≠¾u RôsL[ôp SuÏÑtßYRu êXm, AÕ ùYlTjRÓl× LôlTôLúYûX ùNnÙm. CRu ©\Ï AkRlTWl©uÁÕ £dLu JVo ùUx (chicken wire mesh) ûYjÕAûR ©[ôvPo ùNnYRu êXm £dLu JVoùUx (Reinforcement) BL CÚdÏm.
GdvúTiPÓ Tô≠v¥¬û] G°RôL úUúXAûUdLXôm Utßm AÕ EߧVôL CÚdÏm.©hÓùUu (RôodLh¥) Pd¥u ÁÕ TWl×mùTôÝÕ AÕ Lôl× ùTôÚs Utßm PdÓdÏCûPúV TûNúTôp Jh¥d ùLôiÓRôodLh¥ CûQkÕ ®Óm, CR]ôp R²VôLùYlTRÓl× ©hÓúUu úLôh¥e¡tÏ úUpúRûY«pûX. CkR Lôl× ùTôÚû[£ùUih Utßm ©[ôvPo (A )EúXôLjRLÓ AûPl× êXm ØÝûUùNnÕ®P Ø¥Ùm.
JlTû] EháûW AûUlTRu úSôdLm(Purpose of false ceiling)TRlTÓjRlThP Lôtß Pd¥u Y¯VôLLôtß diffusers êXUôL Aû\ (A )AWeLj§às ÖûZ¡\Õ. AúSL diffusers LsJlTû] EháûWÙPu CûQdLlThÓs[Rôp A§p TpúYß ®RUô]diffusers Ls TpúYß úRûYdÏ HtT AûUdLlTh¥ÚdÏm. JlTû] úUt áûWTRlTÓjRlThP Lôtû\, §Úm©f ùNpÛmLôtßPu LXdLôUp TôojÕd ùLôs¡\Õ.
§ÚmTf ùNpÛm Lôtß ùTôÕYôL ©É]m(A) §ÚmTf ùNpÛm ùTh¥ ¡¬p Y¯VôL(JlTû] úUtáûW«p) ùNpÛm. ØRp¨ûX«p ¨ßYlTh¥ÚdÏm A§L ThNBt\p Lôt±p LXlTRôp, AkR Lôtû\ UßÑZt£ ùNnYÕ YZdLUô] ùNVXôÏm.G]úY §Úm©f ùNpÛm Lôtß LôtßTRlTÓjÕm Aû\dúL §Úm© GÓjÕYWlTÓ¡\Õ. BûX Aû\«p §ÚmTfùNpÛm Lôtû\ JlTû] úUt áûWdÏm,EiûUVô] áûWdÏm CûPúV Es[CûPùY° êXm ùY°úVtßYÕ YZdLm.CkR CûPùY° ©Ç]m (plenum) BÏm.JlTû] EháûW §ÚmTf ùNpÛm LôtßY¯ Gußm A±VlTÓ¡\Õ.
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.12.37
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A±ØLm, ªuNôWj§u ETúVôLeLs, Uô≠dëp, AÔ, ªuNôWmRVô¬jRp, ªuú]ôhPm, ªu]ÝjRm, ªuRûP Utßm ARuAXÏLs T«t£ 1.13.38
ªuNôWm GuTÕ JÚ YûL Bt\p. CÕªLÜm TVàs[ JÚ Bt\p BÏm. CûRLiQôp TôodL CVXôÕ. CÕ ®û[®dLdá¥V TpúYß ®û[ÜLû[ ùLôiÓ RôuCûR SmUôp EQW Ø¥Ùm. ªuNôWmTpúYß YûLVô] Bt\p ARôYÕ ùYlTBt\p, úY§ ®û] Bt\p, AÔ Bt\p,CVk§W Bt\p Utßm úRe¡V Ri½o êXmBt\p B¡V Bt\pLû[ UôtßYRu êXmùT\lTÓ¡\Õ.
ªuNôWjûR ׬kÕ ùLôsYRtÏ AÔ®uLhPûUlûT Su\ôL ׬kÕd ùLôs[úYiÓm.
A¥lTûP«p AÔ®u SÓ®pEhLÚYô]Õ Es[Õ. A§p×úWôhPôuLs, GXdhWôuLs Utßm¨ëhWôuLs Es[]. CkR GXdhWôuLsGu¡\ ùSL¥q ªuòhPm EhLÚ®uAÔûY Ñt±YÚ¡\Õ. ×úWôhPôu Tô£¥qªuòhPm BÏm.
ªuNôW EtTj§dLô] BRôWeLs (Sourcesof electricity)úThP¬ (Battery)C§p úY§ Bt\Xô]Õ ªu]ôt\XôLUôt\lTÓ¡\Õ. CÕ úRûYlTÓm úTôÕªu]ôt\ûX ùLôÓd¡\Õ. CÕ YôL]eLsUtßm ªu]Ô®p TVuTÓjRlTÓ¡\Õ.
ù_]úWhPo (Generator)CÕ JÚ CVk§Wm. Gk§W Bt\pªu]ôt\XôL Uôt\lTÓ¡\Õ.
LôkRl×Xm Utßm (magnetic field) ªu²VdÏ®ûNdÏm (emf) CûPúV ªu LPj§ ÑZÛmúTôÕ çiÓ¡\Õ. CmØû\ûVlTVuTÓj§ GpXô®RUô] AC Utßm DCù_]úWhPo Bt\ûX Uôtß¡u\Õ.
ERôWQm (E.g)• A]p ªu ̈ ûXVm (Thermal power station)• ¿oªu ̈ ûXVm (Hydro power station)• AÔªu ̈ ûXVm (Nuclear power station)• Lôt\ôûX ªu¨ûXVm (Wind power station)• ã¬V Jüõ ªu ̈ ûXVm (Solar power station)ªuNôWj§u TVuLs (Uses of Electricity)1 ûXh¥e þ ®[dÏLs
2 Íh¥e þ ÍhPo, JYu
3 TYo þ úUôhPôo, @úTu
4 ¥Wôd`u þ GXdhúWô úUô¥qv,ªu çd¡, ¡úWu (crane)
5 RLYp þ ùRôûXúT£, Rk§,T¬Uôt\m Yôù]ô≠, JVoùXv
6 ùTôÝÕ þ £²Uô, Yôù]ô≠,úTôdÏ ¥.® (T.V.)
7 UÚjÕYm þ x -úW, ̀ ôd ¥ÃhùUih8 úY§Vp þ úThP¬ Nôo_õe,
ªuØXôm éÑRp9 LôkRm þ RtLô≠L LôkRm10 ùTô±«Vp þ úUd]¥d Ndv
(Magnetic chucks)Tt\ûYl×, Tt\ûYlûTx -úW ùNnRp
Uô≠dëp (Molecule)GpXô ùTôÚsLÞm £±V Uô≠dëp BpB]ûY. ùTtú\ôo Y¯ (parent) ùTôÚsL°uªLf £±V AÔjÕLsLs Uô≠dëpG]lTÓm. Uô≠dëpLs JúW ®RUô] Y¥YmUtßm RuûU«p CÚdÏm. JqùYôÚUô≠dëÛm ARu Rôn Y¯ CVp©Vp UtßmúY§Vp RuûULû[d ùLôi¥ÚdÏm.
AÔ (Atom)AÔ®p 3 ÕLsLs Es[]. AûYVôY]:i ×úWôhPôu (Proton): AÔ®u
SÓlTϧ«p AûUkÕs[ GXdhWôu×úWôhPôu G]lTÓm. AÕ AÔ®u¨ëdXv (ûUVdLÚ) G]lTÓm. C§p×úWôhPôu §WYNUm 1840 UPeÏGXdhWôu §WY NUû] ®P L]Uô]RôLCÚdÏm Utßm AÕ ûahW_uAÔÜdÏ NUUôL CÚdÏm. CÕ Tô£h¥eNôo_ó -I Es[Pd¡ CÚdÏm.
ii ¨ëhWôu (Neutron): CÕ AÔ®p¨ëdXv (ûUVdLÚ) Cp Es[ A¥lTûPÕL[ôÏm. CÕ ¨ëdXv -Cp Es[×úWôhPôu EPu úYLUôL ©ûQdLlTh¥ÚdÏm CRtÏ Nôo_ó GÕÜm¡ûPVôÕ. CÕ áíml (coulomb) -u§WYNUû] A§L¬dÏm.
iii GXdhWôu (Electron): CÕ ̈ ûX«pXôRÕ(A) SLÚm GXdhWôu BÏm. CÕ ̈ ëdXv-I TpúYß ÑtßlTôûR«p Ñt± YkÕùLôiúP CÚdÏm. CÕ ùSL¥q Nôo_ó-I ÑUkÕ ùNpÛm. CÕ ûahW_uAÔ§WYNUj§p 1/1240 TeLôL CÚdÏm.
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117
CRu Nôo_ 1.6 x 10-19 áíml BÏm.
ªuNôWm GqYôß EtTj§ùNnVlTÓ¡\Õ (How electricity is produced)JqùYôÚ AÔ®u SÓ®Ûm ªuNôWmEs[Õ. CÕ GXdhWôu Y¥Yj§p Es[Õ.C§p ̈ ûXVôL Es[ ÕLsLs ×úWôhPôuGußm SLokÕ ùLôiúP CÚdÏm ÕLsLsGXdhWôu Gußm A±VlTÓ¡\Õ. C§p×úWôhPôu Tô£h¥q Nôo_ó BÏm. ùY°®ûN«u LôWQUôL SLÚm GXdhWôuLsÏû\YúRô (A ) A§L¬lTúRô(×úWôhPôàPu Jl©Óm ùTôÝÕ) ̈ LrkÕARu ©\Ï Rôu CWiÓ Nôo_óLÞmCûQ¡u\]. GlùTôÝÕ ×úWôhPôû]®P GXdhWô²u EtTj§ Gi¦dûLÏû\¡\úRô ARu LôWQUôL Tô£h¥qNôo_ó BL B¡\Õ CúR Uô§¬ ×úWôhPôû]®P GXdhWô²u EtTj§ Gi¦dûLA§L¬d¡\úRô ARu LôWQUôL ùSLh¥qNôo_ó BL B¡\Õ. CkR Y¯ Øû\«pªuNôWm AÔ®u êXm EtTj§ B¡\Õ.
GXdh¬dLp LûX ùNôtLs UtßmAXÏLs (Electrical terms and units)ªuNôWj§u A[ÜLs (Quantity ofelectricity)HRôYÕ JÚ LPj§«u êXmGXdhWôuL°u KhPm JÚ ®]ô¥úSWj§p JÚ LPj§«u ÏßdÏ ùYhÓTWlûTd LPkÕ ùNpÛm GXdhWôuL°uùUôjR A[Ü ‘Q’ GuTÕ Nôo_ó BÏm. Utßm‘t’ GuTÕ GÓjÕd ùLôiP úSWm.
G]úY
I = tQ
Q = I x t
ªuNôWj§u SI AXÏ coulomb G]lTÓm.6.24 x 1018 GXdhWôuLs (úRôWôVUôL) JÚcoulomb BÏm.
áíml (Coulomb)JÚ LPj§«u Y¯úV 1 Bm©Voªuú]ôhPm ùNpÛm úTôÕ 1 ®]ô¥«pARu Y¯úV ùNpÛm ªuNôWj§u A[Ü 1coulomb BÏm.
CÕ Bm©Vo ùNLih (As) GußmAûZdLlTÓm. CRu ùT¬V AXÏ Bm©VoaYo (AH) BÏm.
1 AH = 3600 As (ApXÕ) 3600 coulombªu²VdÏ ®ûN (EMF) (Electro motive force)(EMF): ªu Ñt±p ªuú]ôhPm ùNpYRtÏ
úRûYlTÓm ®ûNúV ªu]ÝjR ®ûNG]lTÓm. CûR ‘E’ Gu\ GÝjRôpϱdLXôm. CRàûPV AXÏ úYôph BÏm.
ªu]ÝjR Årf£ (Potential difference) (P.D)ªu Ñt±u CWiÓ ×s°LÞdÏ CûPúVHtTÓm ªu]ÝjR Årf£úV GXdh¬dLpùTôhPuμVp ¥TWuv G]lTÓm. CÕGlùTôÝÕm EMF I ®Pd Ïû\YôLúYCÚdÏm. CRtÏ ùLôÓdLlTÓmªu]ÝjRúU ùTôhPuμVp ¥TWuvBÏm. CRu ϱÂÓ V.
úYôphúP_ó (Voltage): CWiÓ ûXuLs (A)úTv Utßm ¨ëhWp B¡V CWiÓdÏmCûPúV Es[ûY GXdh¬dLpùTôhPuμVp úYôphúP_ó G]lTÓm.CRàûPV AXÏ úYôph BÏm.úYôphúPû_ A[dL úYôph ÁhPoTVuTÓjRlTÓ¡\Õ Utßm Nlû[ùPoª]ÛPu CûQVôL CûQdLlThÓs[Õ.
úYôph (Volt): JÚ ê¥V ªu Ñt±p 1 Kmªu RûP«p 1 Bm©Vo ªuú]ôhPmùNpX úRûYVô] ªu]ÝjRm 1 úYôphG]lTÓm.
ªuú]ôhPm (Current): GXdhWôuL°uKhPúU ªuú]ôhPm G]lTÓm. ApXÕJÚ ®]ô¥ úSWj§p JÚ LPj§«u ÏßdÏùYhÓ TWlûTd LPkÕ ùNpÛmGXdhWôuL°u ùUôjR A[ܪuú]ôhPm G]lTÓm. CRu AXÏBm©Vo ∝ CRu ϱÂÓ I A[dÏm LÚ®AmÁhPo.
Bm©Vo (Ampere): 6.24 x 1018 GXdhWôuLs,ªuLPj§«u ÏßdÏ ùYhÓ TWlûT LPkÕJÚ ®]ô¥ úSWj§p ùNpÛm ùUôjR A[ÜJÚ Bm©Vo G]lTÓm (A) JÚ ê¥V ªuÑt±p 1 Km ªu RûP«p 1 úYôphªu]ÝjRj§p ùNpÛm ªuú]ôhPm 1Bm©Vo G]lTÓm.
ªu RûP (Resistance): JÚ ªu Ñt±pªuú]ôhPjûR G§ojÕ ̈ tÏm LPj§«uTi× AdLPj§«u ªu RûP G]lTÓm.CRu AXÏ = Km (Ω) ªu RûPûV A[dLKm ÁhPo TVuTÓjRl TÓ¡\Õ.
Km (Ohm): JÚ ê¥V ªu Ñt±p CÚ×s°LÞd¡ûPúV 1 Bm©Vo ªuú]ôhPmùNpÛm úTôÕ 1 úYôph ªu]ÝjRúYßTôÓ CÚdÏúUVô]ôp AkR×s°LÞdÏ CûPúVÙs[ ªu RûP 1 KmG]lTÓm.
T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.13.38
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Kªu ®§, LQdÏLs Utßm V.I.R CûP«Xô] E\ÜLs, ùRôPo ªuÑtßLs Utßm CûQªu ÑtßL°u LQdÏLs T«t£ 1.13.39
Kªu ®§ (Ohm’s law)
U = ªu]ÝjRm úYôph -p
l = ªuú]ôhPm Bm©V¬p
R = ªuRûP Kªp
GkRùYôÚ Øtß ùTt\ ªuÑt±Ûm,ªuNôWj§u A¥lTûP A[ÜÚdLs(ªu]ÝjRm, ªuú]ôhPm Utßm ªuRûP) CûYLs JqùYôußdÏm ̈ ûXVô]ùRôPo×Ls EiÓ.
A¥lTûP U§l×Ls (Basic values)
A¥lTûP GXdh¬dLp U§lÀhûPùR°YôdL CûR ÏZôn Ri½¬uAÝjRjÕPu Jl©PXôm.
Ri½¬u AÝjRm þ G X d h W ô uAÝjRm þ ªu]ÝjRm
Ri½¬u A[Ü þ G X d h W ô uKhPm þ ªuú]ôhPm
ÏZô«u ¿o KhPjûR LÝjÕlTϧûVCßd¡d Ïû\jRp þ GXdhWôuKhPj§tÏ RûP þ ªuRûP
E\ÜLs (Relationships)
ªu RûPûV ¨ûXVôL ûYjÕ®hÓªu]ÝjRjûR A§L¬jRôp ªuú]ôhPmA§L¬dÏm.
I ∝ V
ªu]ÝjRjûR ̈ ûXVôL ûYjÕ®hÓ, ªuRûPûV A§L¬jRôp. ªuú]ôhPmÏû\Ùm.
Kªu ®§ (Ohm’s law)
úUtá±V CWiÓ E\ÜLs êXm SUdÏKªu ®§ ¡ûPd¡u\Õ.
CÕ YN§dLôL CqYôß
GÝRlTÓ¡\Õ.
V = R.I.
Uô\ôR ùYlT¨ûX«p JÚ ØtßlùTt\ ªuÑt±p TôÙmªuú]ôhPUô]Õ ªuAÝjRj§tÏ úSo ®¡Rj§Ûm, ªuRûPdÏ G§o ®¡Rj§Ûm CÚdÏm.
Kªu ®§
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ERôWQm (Example)
JÚ Tpl 3.6 úYôp¥p 0.2 Bm©Vo ªuNôWmGÓjÕd ùLôs¡\Õ. Tp©p Es[©XùUuh¥p HtTÓm ªuRûPûVLiÓ©¥. ùLôÓdLlThPûY U = 3.6 V Utßml = 0.2 A. Bm©Vo. RþI LiÓ©¥dL.ùLôÓdLlThPûY V = 3.6 úYôph, l = 0.2Bm©Vo.
BLúY, V = 3.6 V and l = 0.2 A.
BûLVôp, V = l x R
Kmv
ERôWQm (Example)
úXml ©XùUu¥p YZeLlThPÕ. 10.8úYôph B]ôp úYôphúP_ó 12 úYôph BLCÚdL úYiÓm G²p úYôphúP_óCZlûT LiÓ©¥. (TPm 5)
úYôphúP_ó CZl× 12V – 10.8 = 1.2V
YZeLlThP úYôphúP_óªu]ÝjR úYßTôÓ Gußá\lTÓ¡\Õ.
ERôWQm (Example)ûP]úUô®p Eh×\ ªu RûP 0.1 Km,ûP]úUô®u úYôphúP_ó 12V. ùY°l×\ªu Ñtß êXm 20 Bm©Vo ªuNôWmùNÛjRlTÓ¡\Õ. G²p ûP]úUô®púYôphúP_ó GqY[Ü ?
¾oÜ
úYôphúP_ó ¥Wôl = ªuú]ôhPm xEsªu RûP
= 20 x 0.1 úYôph
= 2 úYôph
ERôWQm (Example)úThP¬«u Eh×\ ªu RûP 2 Kmv, CkRúThP¬«p 10 Kmv ªu RûPCûQdLlTÓ¡\Õ. CR]ôp 0.6 Bm©VoùT\lTÓ¡\Õ. úThP¬«u EMFþI LiÓ©¥?(TPm 6)
ªu]ÝjR úYßTôÓ = ªuú]ôhP TônÜx ªu RûP (P.D = Current flowing x Resistance)
= 0.6 A x 10Ω
= 6 úYôph
V.D = ªuú]ôhP TônÜ x úThP¬«pEh×\ ªuRûP
= 0.6 x 2 úYôph
= 1.2 úYôph
úThP¬«u EMF = (6.00 + 1.2) úYôph
= 7.2 úYôph
GpXô ªu RûPL°u áhÓj ùRôûLùUôjR ªu RûPdÏ NUm. CmØû\«p ªuRûPLs, ØRp úXô¥u LûP£ Øû]ÙPuCWiPôYÕ úXô¥u BWmT Øû]ÙPuCûQdLlTÓ¡\Õ Utßm GpXôúXôÓLÞm Øû]dÏ Øû] CûQdLlThÓCÚdÏm.
ùRôPo CûQl× Øû\«u AûUl×:
• RûPL°u Y¯úV ùNpÛm ªuú]ôhPmJúW A[YôL CÚdÏm.
• JqùYôÚ úXôÓLÞdÏ CûPúVVô]ªu]ÝjRm RûPL°u A[®túLtTT¡okÕ ùLôs[lTÓm.
ªu RûP CûQl×Ls (Resistanceconnections)
U = ªu]ÝjRm (úYôp¥p)
R = ªuRûP (Kªp)
I = ªuú]ôhP CuPu£h¥(Bm©V¬p)
ùRôPo CûQl× Øû\ (Series Connection)
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• JqùYôÚ úXôh úYôphúP_õu áhÓùRôûL ùNÛjRlThP úYôphúP_õdÏNUm.
• ªu Ñt±u ùUôjR ªu RûP A§Ûs[RûPL°u áhÓj ùRôûLdÏ NUm.
l = l1 = l2 = ...V = V1+ V2+ ...R = R1+ R2+ ...
CûQ CûQl× Øû\ (Parallel connection)CmØû\«p ªu RûPL°u JjR Øû]LsCWiÓ Ï±l©hP ×s°LÞdÏ CûPúVCûQdLlThÓ CÚdÏm.
CûQ CûQl× Øû\«u AûUl×(Features of parallel connection):• JqùYôÚ úXô¥Ûm ªuú]ôhPm
TônYÕ úXô¥u ªu RûPûVlùTôÚjRRôÏm.
• JqùYôÚ ªu]Ýj§tÏ CûP«Ûs[úXôÓm NU A[®Ûm Utßm AkR ªuÑtßdÏ ùLôÓdLlThP ªu]ÝjRj§tÏNUUôLÜm CÚdÏm.
• ùUôjR ªuRûP«u áhÓ U§l× CûQCûQl× ªu Ñt±p Es[ ªLf£±VªuRûPûVd Lôh¥Ûm £±VRôLCÚdÏm.
• CûQ CûQl× ªuÑt±p Es[ ùUôjRªu RûPL°u G§o ®¡Rm ùUôjR ªuRûPL°u G§o ®¡Rj§u áhÓjùRôûLdÏf NUUôL CÚdÏm.
l = l1 + l2 + ...V = V1 = V2 ...
ERôWQm (Example)4 Kmv Utßm 6 Kmv B¡V CWiÓªuRûPLs CûQ CûQl× Øû\«pCûQdLlThÓs[Õ. ùUôjR ªu RûPûVLiÓ©¥.
(CûQ CûQl×)
BûLVôp
BûLVôp R Kmv = 2.4 Kmv
ERôWQm (Example)2 Utßm 4 Kmv B¡V CWiÓ ªu RûPLs6 úYôph úThP¬«p CûQdLlThÓs[Õ.
þ ùUôjR ªu RûPûV LiÓ©¥
þ ùUôjR ªuú]ôhPm Utßm Tϧªuú]ôhPm LôiL.
¾oÜ
ùUôjR ªu RûP
3Ω11=
34=R
4Ω3=
41+2=
41+
21=
R1+
R1=
R1
tot
21tot
I ùUôjRm= I1 + I2 ªuú]ôhPm
B]ôp
I ùUôjRm = 3A+1.5A
= 4.5 Bm©Vo
§\]ônÜ T«t£L°p ùLôÓdLlThPªu RûP«p ©XùUuh Es[ TplUtßm Ut\ ªuú]ôhPjûRTVuTÓjÕm LÚ®Ls ARôYÕ aôou(Horn) ûYlTo (Wiper) úTôu\ YôL]LÚ®LÞm Es[RôLd ùLôs[Üm.
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ªuNd§, Bt\p Utßm ARu AXÏLs, §\]ônÜ T«t£ UtßmLQdÏLs T«t£ 1.13.40
V - ªu]ÝjRm (Volts) V
i - ªuú]ôhP CuPu£h¥ (Bm©Vov) (Current Intensity) (Ampheres) A
P - §\u (Yôhv, ¡úXô Yôhv) (Power)(Watts, Kilowatts) W, kW
W - úYûX, Bt\p (Yôh aYo, ¡úXô YôhaYo) wh, Kwh
t - úSWm (aYo) h
ùTôÚû[ JÚ ÁhPo çWj§tÏ SLojÕm§\àdÏ 1 Yôh Guß ùTVo.. ªu Ñt±pªu CVdÏ ®ûN, ªu RûPûV G§od¡u\ÕUtßm úYûX ùNn¡\Õ. ªu Ñt±p ùNnÙmúYûXARu ªuú]ôhPm Bm©VûWlùTôÚjRÕ. ªu CVd¡ ®ûN«p JÚ úYôphGuTÕ, JÚ Bm©Vo ªuú]ôhPj§u êXmJÚ Yôh §\û] ùY°lTÓjÕYRôÏm.
G]úY §\u = úYôphúP_ó (x)ªuú]ôhPm
Voltage x CurrentP= U x l
Yôhv£p §\u = ªu]ÝjRm (úYôph) xªuú]ôhPm (Bm©Vo)
Power in Watts = Voltage in Volts x Current in Ampheres
ªu úYûX, Bt\p (Electric work, energy)ªu úYûX (A) Bt\p GuTÕ ªu]ôt\pUtßm GÓjÕd ùLôiP úSWj§u ùTÚdÏùRôûLVôÏm.
Jod Cu Yôh ùNLih = TYo Cu Yôhvx ûPm Cu ùNLih
Work in Watt seconds = Power in Watts x time in sec-onds
W = P x t
1 _øp GuTÕ 1 Yôh x 1 ùSô¥, CÕ ªLf£±VÕ. G]úY 1 Yôh aYo Utßm 1 ¡úXôYôh aYo Gu\ ùT¬V AXÏLsTVuTÓjRlTÓ¡\Õ.
1 W.h = 3600 Yôh ®]ô¥
1 Kwh = 1000 Wh = 3600000 Yôh ®]ô¥
ªu §\u (Electric Power)
CVk§W®Vp ùNVpTôh¥p úYûXùNnVlTÓm ÅRúU §\u G]lTÓm. ªuÑt±p áP ªu §\²u AXÏ 1 Yôh.CVk§W®Vp ùNVpTôh¥p JÚ ®]ô¥úSWj§p, JÚ ¨ëhPu (N) ®ûN«p JÚ
CVk§Wm Utßm ªu A[ÜL°u EYûULs AhPYûQ«p ùLôÓdLlThÓs[Õ(Table of analogies between mechanical and electrical quantities)
CVk§W A[ÜLs AXÏ (Unit) ªu A[ÜLs AXÏ (Unit)(Mechanical quantity) (Electrical quantity)®ûN ('F’) ¨ëhPu (N) ªu]ÝjRm (‘V’) V
m/s ªuú]ôhPm i A
úSWm t ®]ô¥Ls úSWm t ®]ô¥Ls
§\u P = F x v N §\u P = V x i W = V x A
Bt\p = F x v x t j = Nm Bt\p W = V x i x t j = W x s
§ûN úYLm v =CPl ùTVof£
LôXm
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122
W = V I= I2 R
= R
V 2
2
2
IWWV
IVR
=
=
=
ϱl×: ÖLoúYôÚdLô] ªuLhPQm Kwh þp LQd¡PlTÓ¡\Õ.CÕ SôÓ Utßm Uô¨Xj§tÏUô¨Xm UôßThÓ CÚdÏm.
ERôWQm (Example)
1 ªuú]ôhPm 0.25 Bm©Vo Utßmªu]ÝjRm 240 úYôph ®[d¡uBt\p úWh¥eûL LQd¡Ó.
P = V x I
V = 240 úYôph
I = 0.25 Bm©Vo
BûLVôp,
Bt\p = 240 úYôph x 0.25 Bm©Vo
= 60 úYôph Bm©Vo
B]ôp, 1 Yôh = 1 úYôph x 1 Bm©Vo
BûLVôp, Bt\p = 60 Yôhv
2 15 Bm©Vo ªuú]ôhPm 10 Kmvªu RûP Y¯VôL ùNp¡\Õ. NUuTÓjRlThP ªu A[ûY ¡úXôYôh¥p LQd¡Ó.
ùLôÓdLlThPûY
R = 10 Utßm I = 15 Bm©Vo
Bt\p = V x I = I x R x I = I2 x R
BûLVôp,
Bt\p = 152 x 10 = 2250 Yôhv = 2.25 ¡úXôYôhv
3 ûX²p ªu]ÝjRm 200 úYôph,®[dÏ TVuTÓj§V ªuú]ôhPm 0.91Bm©Vo, ®[dÏ 12 U¦úSWm TVuTôh¥p CÚkRÕ. ùLôÓdLlThPúYôph = 200 úYôph
úYûXûV Whþp LQd¡PÜm
V = I R
WRIW
=
=
RWVWRVI
=
=
=
I = 0.91 Bm©Vo
t = 12 U¦ úSWm
BûLVôp
Bt\p = V x I = 200 úYôph x 0.91 Bm©Vo
= 182 Yôhv
BûLVôp,
úYûX = P x t = 182 Yôhv x 12 U¦úSWm
= 2184 Yôh aYo
4 105 ¡úXô Kmv/ 0.08 Bm©Vo G] N¬ùNnVd á¥V ªu RûPVõp ϱdLlThÓs[Õ. ARàûPV ϱdLlThPBt\p GqY[Ü?
ùLôÓdLlThPûY,
R = 1.5 ¡úXô Kmv (k Ohms)
I = 0.08 Bm©Vo (A)
P = ûV LiÓ©¥
V = R x I = 1500 ¡. Kmv. 0.08 Bm©Vo (A ) = 120 úYôph
(P = V x I) = 120 úYôph 0.08 Bm©Vo = 9.6Yôhv ARtÏ T§XôL
P = 12.R = (0.08 Bm©Vo A)2
= 1500 Kmv = 9.6 Yôhv
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5 220 v ªu]ÝjRj§p 110ΩΩΩΩΩ ªu RûPEûPV ªu Cv§¬ ùTh¥ùNVpTÓ¡\Õ. ªu Cv§¬ ùTh¥TVuTÓj§V ªuú]ôhPm UtßmBt\ûX LiÓ©¥
ªu Cv§¬ ùTh¥«u ªu RûP
(R) = 110 Km
ªu]ÝjRm (V)ó = 220 úYôph
ªuú]ôhPm (I) = RV
= 200/110 = 2 Bm©Vo
Bt\p (w) = V x I
= 220 x 2
= 440 Yôh
6 240 úYôphúP_õp SôuÏ 1000 Yôh,Utßm 180 úYôph ÍhPÚm ùRôPoCûQl©p CûQdLlThÓs[Õ.ªuú]ôhPj§u A[Ü 15 Bm©VoG²p ùUôjR §\û]d LiÓ©¥?
CûQl× = ùRôPo
ÍhP¬u Gi¦dûL = 4
ÍhP¬u §\u (W) = 1000 Yôhv
ÍhP¬u ªu]ÝjRm = 180 úYôph
Nlû[ ªu]ÝjRm = 240 úYôph
ÍhP¬u ªu RûP (R) =
=10324
1000180 x 180
=
= 32.4 Kmv
ùUôjR ªu RûP = 32.4 x 4 = 29.6 Kmv
ùUôjR ªuú]ôhPm (I) = RV
= 129.6240
= 1.85 Bm©Vo
ùUôjR §\u (W) = V x I
= 240 x 1.85 = 444 Yôh
7 40 Yôh ÏZp ®[d¡tÏ 0.1 Bm©Voªuú]ôhPm úRûYlTÓ¡\Õ. AÕJüõoYRtÏ GqY[Ü ªu]ÝjRmúRûY?
®[d¡u §\u (W) = 40 Yôh
ªuú]ôhPm (I) = 0.10 Bm©Vo
ªu]ÝjRm (V) = IW
= 0.140
= 400 úYôph
8 15 ϧûW Nd§ ùLôiP úUôhPôoSôs JußdÏ 6 U¦ úSWm ÅRm 15SôhLs CVeÏ¡u\Õ. JÚë²h¥tLô] LhPQm 3 ìTôn, G²p.úUôhPôo CVeÏYRtÏ GqY[ÜìTôn BÏm.
úUôhPô¬u §\u (w) = 15 HP
= 15 x 746 = 11,190 Yôh
JÚ Sô°u TVuTôÓ= 11,190 x 6
= 67140 Yôh
= 67.14 ¡úXô Yôh
15 SôhLÞdLô] TVuTôÓ= 67.14 x 15
= 1007 ¡úXô aYo (A) ë²h
JÚ ë²h¥u ®ûX = Rs. 3
ùUôjR TVÉh¥tLô] ®ûX
= 3 x 1007 = Rs. 3021
1 §\]ônÜ T«t£ (Assignment)
1 ªu RûP (R)= 40 Kmv
ªuú]ôhPm (I)= 6.5 Bm©Vo
ªu]ÝjRm (V)= ______ úYôph
2 ªu]ÝjRm (V)= 6 úYôph
ªuú]ôhPm (I)= 0.5 Bm©Vo
ªu RûP(R) = ______ Kmv
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3 ªu]ÝjRm (V)= 220 úYôph
ªu RûP(R) = 820 Kmv
ªuú]ôhPm (I)= ______ Bm©Vo
4 ªuú]ôhPm (I)= 4.5 Bm©Vo
ªu]ÝjRm (V)= 220 úYôph
ªu RûP(R) = ______ Kmv
5 ªu RûP (R)= 50 Kmv
ªu]ÝjRm (V)= 220 úYôph
ªuú]ôhPm (I)= _____ Bm©Vo
6 ªu]ÝjRm (V)= 110 úYôphªuú]ôhPm (I)= 4.55 Bm©Voªu RûP(R) =_____ Kmv
7 ªu RûP (R)= 250 Kmv
ªuú]ôhPm (I)= 0.44 Bm©Vo
ªu]ÝjRm (V)= ______ úYôph
8 ªuú]ôhPm (I)= 11.5 Bm©Vo
ªu]ÝjRm (V)= 380 úYôph
ªu RûP(R) = ______ Kmv.
9 ªu RûP (R)= 22 Kmv
= 7.8 Bm©Vo
(ªu]ÝjRm¥Wôl)
ªu]ÝjRm (V)= ______ úYôph
2 §\]ônÜ T«t£ (Assignment)1 ªu RûP (R1 )
= 12 Kmv
ªu RûP (R2 )= 22 Kmv
ªu RûP (R3 )= 24 Kmv º¬v
ªu RûP (R) =______ Kmv
2 ªu RûP (R1 )= 15 Kmv
ªu RûP (R2 )= 25 Kmv
ªu]ÝjRm (V)= 220 úYôph
ªu]ÝjRm (V1)= ______ úYôph
ªu]ÝjRm (V2)= ______ úYôph
3 ªu]ÝjRm (V)= 220 úYôph(R1 ) = 40 Kmvªu]ÝjRm (V1 )= 100 úYôph(ùRôPoCûQl©p)R2 = ______ Kmv
4 ªu]ÝjRm (V)= 80 úYôph(I) = 2 A(R1)= 30 Kmv(ùRôPoCûQl©p)(R2) = ______ Kmv
5 ªu RûP (R1 )= 6 Kmvªu RûP (R2 )= 12 Kmv
ªu RûP (R3 ) = 18 Kmv CûY êußm CûQ CûQl×L[ôÏm ªu RûP (R) = ______ Kmv
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6 ªu RûP (R)= 6 Kmv
ªu RûP (R1,R2,R3)CûQ CûQl×Øû\
ªu RûP (R1)= 12 Kmv
ªu RûP (R2)= 16 Kmv
ªu RûP (R3)= ______ Kmv
7 ªu RûP (R1)= 40 Kmv
ªu RûP (R2)= 60 Kmv
ªu]ÝjRm (V)= 220 úYôph
ªuú]ôhPm (I)= ______ Bm©Vo
ªuú]ôhPm (I1)= ______ Bm©Vo
ªuú]ôhPm (I2 )= ______ Bm©Vo
3 §\]ônÜ T«t£
1 TVuTÓjRlThPªuú]ôhPm
(I) = 0.136 Bm©Vo
ªu]ÝjRm (V)= 220 úYôph
TYo (P)= _____ Yôhv
2 TYo (P)= 500 Yôhv
(I) = 2.27 Bm©Vo
ªu]ÝjRm (V)= ______ úYôph
3 TYo (P)= 750 Yôhv
ªu]ÝjRm (V)= 220 úYôph
(I) = ______ Bm©Vo
4 TYo (P)= 60 Yôhv
ªu]ÝjRm (V)= 200 úYôph
ªuRûP (W)R = _______ Yôh
5 ªuú]ôhPm (I)= 0.455 Bm©Vo
ªu RûP (R)= 484 Kmv
TYo (P)= ______ Yôhv
6 TYo (P) = 550 Yôhv
ªu RûP (R)= 22 Kmv
ªuú]ôhPm (I)= ______ Bm©Vo
7 TVuTÓj§V TYo(P) = 1.8 ¡úXôYôhv
ªu RûP (R)= 8 Kmv
ªu]ÝjRm (V)= ______ úYôph
8 TVuTÓjRlThPTYo ‘P’ = 2 ¡úXôYôhvªu]ÝjRm (V)= 220 úYôph(Íh¥eG≠ùUihªu]ÝjRm)(R) = ____ Yôhv
9 TYo (P) = 100 Yôhv
úSWm (t) = 1U¦úSWm
TVuTÓj§VBt\p = ______¡úXôYôh aYo
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10 TVuTÓj§VBt\p ‘W’ = 1¡úXô Yôh aYo
TYo (‘P’)= 100 Yôhv
úSWm (t) = ________U¦úSWm
11 Yôhv (W) = 1.5¡úXô Yôh aYo
úSWm (t) = 45 ̈ ªPm
TYo (P) = ______ ¡úXôYôh
12 G]o_õ ÁhP¬uA[ÜLsW1 = 6755.3 kWhA§L¬dLlThPW2 = 6759.8 kWh
úSWm(t) = 45¨ªPm
TYo (P) =______ ¡úXôYôh
13 TVuTÓj§VBt\p (‘P’)= 6.2 ¡úXôYôh
úSWm (t) = 8 U¦úSWm
JÚ ¡úXô YôhU¦ úSWj§tÏ
= 1.25 ìTôn
ùUôjR ®ûX
= ______ ìTôn
14 ªuú]ôhPm (I)= 5.45 Bm©Vo
ªu]ÝjRm (V)= 220 úYôph
TVuTÓj§VBt\p
= 1 ¡úXô YôhaYo
úSWm (t) = ________U¦úSWm
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LôkR çiPp, Ru ªu çiPp Utßm TWvTW ªu çiÓ§\uUtßm ªu CVdÏ ®ûN EtTj§ T«t£ 1.13.41
LôkR çiPp (Magnetic induction)
JÚ CÚm×j çi¥u AÚúL, LôkRj§û]ùLôiÓ YÚm ùTôÝÕ LôkRj çiPpHtThÓ CÚm×jÕiÓ LôkRUûP¡\Õ.EiûU«p, CÚm×jÕiûP Ruû] úSôd¡CÝdÏm Øu, LôkRm CÚm×jÕi¥u G§oÕÚYj§p çiPûX HtTÓjÕ¡\Õ UtßmG§ùW§o ÕÚYj§u Dol×jRuûULôWQUôL LôkRm CÚm×jÕiûP Ruû]úSôd¡ CÝd¡\Õ. CRtLôL LôkRmCÚm×ÕiûP ùRôP úYi¥VAY£VªpûX.
TpúYß ªu A[®Óm LÚ®L°p TôoLôkReLÞPu ùUuûUVô] CÚm×jÕÚYjÕiÓLs TVuTÓjRlTÓ¡u\].TVuTÓjÕm LôkRj§tÏ JÚ Ï±l©hPY¥Ym ùLôÓlTRtÏ, CqYûLÕÚYjÕiÓLs TVuTÓjÕYÕLôkRjÕiP≠u LÚjÕÚYj§uA¥lûP«XôÏm.
LôkRl×Xj§u ÅfÑ (Intensity of magneticfield)
LôkRl×Xj§p ûYdLlThÓs[ AXÏÕÚYj§p HtTÓm ®ûNVô]ÕLôkRl×Xj§u ÅfÑ G]lTÓm. CÕ “H” Gu\GÝj§]ôp ϱdLlTÓm. CRu AXÏ Wb/mBÏm.
ªuLôkR çiPp RjÕYm Utßm ®§Ls(Principles and laws of electromagnetic induction )
JÚ ªuLPj§«p UôߧûN ªuú]ôhPmùNpÛm úTôÕ TôWúP«u ªu LôkRçiPp ®§ ARtÏ ùTôÚkÕm.
TôWúP«u ªuLôkR çiPp ®§(Faradays’ Laws of Electromagnetic Induction))
TôWúP«u ØRp ®§ (Faraday’s First Law):LôkRd úLôÓLû[ LPj§ ùYhÓYRôúXô,LPj§ûVf Ñt±Ùs[ LôkRd úLôÓLs ARuU§l©Ûm §ûN«Ûm UôßRp AûPkRôúXôLPj§«p ªu CVdÏ®ûN çiPlTÓ¡\Õ.
TôWúP«u CWiPôYÕ ®§ (The SecondLaw): LPj§«p çiPlTÓm ªu CVdÏ®ûN ϱl©hP úSWj§p LPj§«u úUpHtTÓm LôkRd úLôÓL°u UôßTôh¥uA[®tÏ úSo ®¡Rj§p CÚd¡\Õ.
Cq®WiÓ ®§«uT¥ LPj§«pªuú]ôhPm EiPô¡\Õ.
ûP]ªd ªu]ÝjRm (Dynamically InducedEMF)
úUtLiP ®§Øû\dúLtT çiPlTÓmªu]ÝjRUô]Õ JÚ ¨ûXVô]LôkRl×Xj§p JÚ ªu LPj§ûV ×Xj§tÏùNeÏjRôL SLW ûYlTR]ôúXô, ¨ûXVôLEs[ JÚ ªuLPj§ ÁÕ UôßTÓmLôkRl×XjûR HtTÓjÕYRôúXô, JÚªu]ÝjRjûR HtTÓjR Ø¥Ùm. ̈ ûXVô]LôkRl ×Xj§p SLÚm ªu LPj§ûV ùLôiÓEiPôdÏm ªu]ÝjRj§tÏ ûP]ªdªu]ÝjRm Guß ùTVo. ERôWQm :ù_]úWhPo.
¨ûXVô] ªu]ÝjRm (Statically InducedEMF)
¨ûXVôL Es[ ªuLPj§ ÁÕ UôßThÓdùLôi¥ÚdÏm LôkR×XjûR ùNÛj§ ARuêXm ªu]ÝjRm ùTßYRtÏ ¨ûXVô]ªu]ÝjRm (Statically Induced EMF) Guß ùTVo.ERôWQm: ¥Wôuv@TôoUo.
¨ûXVô] ªu]ÝjRm (Statically InducedEMF): UôßTÓm LôkRl×Xj§u êXm¨ûXjÕs[ JÚ ªuLPj§«p ªu]ÝjRmHtTÓjÕYRtÏ ¨ûX ªu]ÝjRm GußùTVo.
CÕ @TôWúP -«u EMF ®§«u CWiÓYûLVô] ¨ûXVô] ªu]ÝjRm ¸úZ®[dLlThÓs[Õ.
1 Ru çiPp ªu]ÝjRm (Self inducedemf) Lôl©PlThP JúW Lm©fÑÚ°pHtTÓm ªu]ÝjRm.
2 TWvTW çiPp ªu]ÝjRm (Mutuallyinduced emf) AÚLÚúL Es[ Lm©fÑÚ°pJÚ Lm©fÑÚ°p Uôß §ûN ªuú]ôhPmùLôÓjÕ AÓjR Lm©fÑÚ°p AúR UôߧûN ªuú]ôhPjûR GÓdÏmØû\VôÏm.
Ru ªu çiPp (Self-induction): LPj§«uY¯VôL UôߧûN ªuú]ôhPm ùNÛjÕmúTôÕ LôkRj§ûN«u §ûNVô]ÕUôßTÓ¡\Õ. C§p ªuú]ôhPm TôÙm§ûNÙm LôkRl×Xj§u §ûNûVÙm A±kÕùLôs[ Ø¥Ùm.
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128
JÚ ØÝ ûNd¡°p LôkRl×XUô]ÕLPj§ûV Ñt± HtTÓ¡\Õ. CÕG§o§ûN«Ûm §ÚmT HtTÓ¡\Õ.AlùTôÝÕ LôkR×Xj§u ØÝ A[Üm"0"YôL Es[Õ. LôkRd úLôÓL[ô]ÕLPj§ûV ûUVUôLd ùLôiÓ ùY°«pÑtß¡u\]. CkRd úLôÓLs LPj§ûVùYhÓ¡u\].
Ruªu çiPp (Self induction)
TôWúP«u ®§dÏ CQeL LPj§Vpªu²VdÏ ®ûN çiPlTÓ¡\Õ. CúRúTôp LôkRl ×Xj§p ÁiÓm LôkR ®ûNdúLôÓLs LPj§ûV ùYhÓYRôp ÁiÓmJÚ Øû\ ªu²VdÏ ®ûN çiPlTÓ¡\Õ.CRtÏ Ruªu çiPp Guß ùTVo.CmØû\«p HtTÓm ªu²VdÏ ®ûNVô]Õ¨ûXVô] ªu²VdÏ ®ûNVôÏm. (TPm 1)
TWvTW ªuçiÓ §\u (Mutual Inductance):ùTôÕYô] LôkR úLôÓL°]ôp JußApXÕ ARtÏ úUtThP Lô«pLsLôkRj§]ôp CûQdLlThPôp CûYLsTWvTW ªuçiÓ §\u ÏQô§NVeLû[ùTtßs[Õ Guß A±VXôm. CkRA¥lTûP RjÕYj§p ¥WôuvTôoUo,úUôhPôo, ù_]úWhPo Utßm CRW ªuNôR]eLs CVeÏ¡\Õ. TWvTW ªuçiP≠uT¥ JÚ Lô«≠p TôÙmªuú]ôhPjRôp TdLj§Ûs[ Lô«≠pªu]ÝjRm çiPlTÓ¡\Õ.
TPm 2þp Lôi©jÕs[T¥ Lô«p L1 þ²pTôÙm ªuú]ôhPjRôp LôkR UiPXmARû] Ñt± HtTÓ¡\Õ. úUÛm £X LôkRúLôÓLs Lô«p L2 Y¯VôLÜm Tôn¡\Õ.CR]ôp TWvTW ªuçiÓ §\uHtTÓ¡\Õ. Lô«p Ju±u ªuú]ôhPm N1
ÑtßLû[Ùm Lô«p CWi¥u ªuú]ôhPmN2 ÑtßLû[Ùm ùLôiÓs[Õ. CR]ôpTWvTW ªu çiÓ §\u M EiPô¡\Õ.
CWiÓ Lô«pL°Ûm EiPôÏm TWvTWªuçiÓ §\û] 'M' A[dL CWiûPÙmùTôÕYô] Nôlh CÚm× úLôo (soft iron core)ÁÕ ûYjúRô ApXÕ ÑtßdL°uGi¦dûL LQd¡hÓ A±kÕ ùLôs[Xôm.CÕ ¥WôuvTôoU¬p Es[ûRúTôpCÚdÏm.
CWiÓ Lô«pLÞdÏm CßdLUôLûY«i¥e ùNnVlTÓ¡\Õ. AR]ôpÄdúL_ó_ôp HtTÓm CZl× ªLÜm Ïû\Ü.CWiÓ Lô«pLÞdÏ CûPúV LôkRúLôÓL°u CûQl× HtThÓs[Õ GußLÚj§p ùLôiÓ TWvTW ªuçiÓ§\u'M' ûV A±VXôm.
CVdL ªuçiPp §\u (Dynamicallyinduced EMF)
ù_]úWhPo (Generator): CVk§W Bt\ûXªu Bt\XôL Uôtßm CVk§Wm ªuNôWù_]úWhPo BÏm.
ù_]úWhP¬u RjÕYm (Principle of theGenerator): CVk§W Bt\ûX ªu Bt\XôLUôtßm ù_]úWhPo @TôWúP þ®uªuLôkR çiPp ®§«u RjÕYj§uA¥lTûP«p CVeÏ¡\Õ.
@TôWúP®u ªuLôkR çiPp®§(Faraday’s laws of electromagnetic induction):
CWiÓ ®§Ls Es[]
ØRp ®§
• LôkRj úLôÓLû[ LPj§ ùYhÓYRôúXô,LPj§ûVf Ñt±Ùs[ LôkRd úLôÓLsARu U§l©Ûm §ûN«Ûm UôßRpAûPkRôúXô LPj§«p ªu CVdÏ ®ûNçiPlTÓ¡\Õ.
CWiPôm ®§
• LPj§«p çiPlTÓm ªu CVdÏ ®ûNϱl©hP úSWj§p LPj§«u úUp
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HtTÓm LôkRd úLôÓL°u UôßTôh¥uA[®tÏ úSo ®¡Rj§p CÚd¡\Õ.
ªu CVdÏ®ûN«u YûLLs (Types ofemf): @TôWúP ®§L°uT¥, ªu CVdÏ®ûNûV (emf) ̈ ûXVô] LPj§«u UôßThPLôkRl×XjûR CûQlTRu êXúUô (A)LôkRl×Xj§tÏm LPj§dÏm CûPúVE\ÜØû\ SLo®u êXúUô çiP Ø¥Ùm.
CVdLj§u êXm çiPlThP ªuCVdÏ ®ûN (Dynamically induced emf): TPm3a -p Lôh¥Ùs[ T¥ ¨ûXVô]LôkRl×Xj§p Es[ LPj§ SLoYRuêXUôL ªu CVdÏ ®ûN çiPlTPXôm(A) TPm 3b -p Lôh¥Ùs[T¥ ¨ûXVô]LPj§«p LôkRl ×Xj§û] SLojÕYRuêXUôLúYô çiPlTÓm ªu CVdÏ®ûN,CVdLj§u êXm çiPlThP ªu CVdÏ®ûN G]lTÓm.
3a Utßm 3b TPj§p Lôh¥Ùs[ûRl úTôpCWiÓ Øû\«Ûm LPj§ ®ûN«uúLôÓLû[ ùYhÓYRu êXm ªu CVdÏ®ûNûV çiPXôm úUÛm ªu CVdÏ®ûN«u CÚlûT A±kÕ ùLôs[“úLpYú]ô ÁhPo êXm - ‘G p Es[Øs°u ®XLp êXm LiÓ ùLôs[ Ø¥Ùm.CkRj RjÕYm DC Utßm AC ù_]úWhP¬pªuNôWm RVô¬dLl TVuTÓjRlTÓ£\Õ.
¨ûXjRuûU«u êXm çiPlThPªu CVdÏ ®ûN (Statically induced emf):TPm 2 -p Lôh¥Ùs[T¥, JÚ ¨ûXVô]LPj§«u úUp HtTÓm úYßThPLôkRl×Xj§u êXm çiPlTÓm ªuCVdÏ ®ûN, ¨ûXj RuûU«u êXm
çiPlThP ªu CVdÏ®ûN G]lTÓ¡\Õ.C§p LôhPlThÓs[ Lô«p 1 Utßm Lô«p2 Juû\ Juß ùRôhÓd ùLôsY§pûXUtßm AYt±²ûPúV GkR ªu CûQl×mCpûX.
TPm 4 -u T¥ Lô«p 1 -p ETúVôLlTÓjRlTÓm TôhP¬ (DC) Nlû[ êXm Lô«p 2 -pªu CVdÏ ®ûN çiPlTÓ¡\Õ. (Ñ®hf“S” êÓm ùTôÝÕ (A) §\dÏm ùTôÝÕ). JÚúYû[ Ñ®hf -I ¨WkRWUôL ê¥úVô (A)§\kR ̈ ûX«úXô ûYj§ÚkRôp Lô«p 1 -pEtTj§VôÏm LôkRl×Xm ̈ ûXVô]RôL (A)é_ó_÷VUôL CÚdÏm úUÛm Lô«p 2 -p ªuCVdÏ ®ûN çiPlTPôÕ. G]úY DC ªuÑt±p Lô«p 1 -u NôdëªûP êÓYúRô (A)§\lTRu êXm LôkRl×Xm úYßTÓmùTôÝÕ ªu CVdÏ ®ûN çiPlTÓ¡\Õ.
Uô\ôL TPm 4 -p Lôh¥Ùs[T¥ úThP¬Utßm Ñ®hf -I Lô«p 1 -p CÚkÕ ALt±®hÓ AûR AC TYo Nlû[ÙPuCûQjÕ®PXôm. CqY\ôL Lô«p 1 -I ACTYo Nlû[«p CûQlTRôp Lô«p -2 EPuCûQdLlThP Lô«p 1 -p EtTj§ùNnVlTÓm UôßTÓm LôkRl ×Xm, Lô«p -1 AC TYo Nlû[ÙPu CûQdLlThÓs[YûW Lô«p -2tÏ ªu CVdL ®ûN çiPûXùLôÓjÕd ùLôiúP CÚdÏm. CkRjRjÕYm Transformers Guß ùNôpXlTÓ¡\ ªuUôt±«p TVuTÓjRlTÓ¡\Õ.
CVdLj§u êXm çiPlThP ªuCVdÏ ®ûN EtTj§ ùNnRp (Production ofdynamically induced emf): GlùTôÝÕ JÚ LPj§LôkRl ×XjûR ùYhÓ¡\úRô AlùTôÝÕARtÏs CVdLj§u êXm çiPlThPªu CVdÏ ®ûN EtTj§ ùNnVlTÓ¡\Õ.AkR LPj§dLô] ªu ÑtßêPlTh¥ÚkRôp CkR CVdÏ ®ûN AkRªu Ñt±p ªuú]ôhPjûR ®û[®d¡\Õ.
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CVdLj§u êXm çiPlThP ªu CVdÏ®ûNûV EtTj§ ùNnV úRûYVô]ûY
• LôkRl×Xm
• LPj§
• LôkRl×Xj§tÏm, LPj§dÏmCûPúVVô] E\Ü SLoÜLs
ùRôPo×ûPV LôkRl ×XjÕPu ‘V’ ùRôPoקûNúYLm Es[ LPj§ SLokRôp, AR]ôpçiPlTÓm ªu CVdÏ ®ûN ‘e’ Vô]Õ.
= BLV Sinθ úYôph BL CÚdÏm.
C§p
B = LôkRl×X APoj§ (ùPvXô - ®pA[®PlTÓ¡\Õ).
L = LôkRl×Xj§p LPj§dÏ úRûYVô]¿[m (ÁhP¬p).
V = LPj§dÏm LôkRl ×Xj§tÏmCûPúVVô] ùRôPo× §ûNúYLm (ÁhPo/ùNLi¥p).
θ = LôkRl ×XjûR LPj§ ùYhÓm úLôQm.
CkR U§l×Lû[ JÚ ¡Wôl Rô°p (graph sheet)T§®ÓYRu êXm, ºWô] LôkRl×Xj§p NUtßm S ÕÚYeLs ÑZÛm ùTôÝÕLPj§«u Esú[ HtTÓm ªu CVdÏ®ûN«u çiPp ûNu úYq Y¥®p (sinewave pattern) ©W§¨§jÕYlTh¥ÚlTûRLôQXôm.
CqYô\ô] ùNVpØû\«u A¥lTûP«pçiPlThP ªu CVdÏ ®ûNA¥lTûP«p UôßTÓm CVp©p CÚdÏm.úUÛm CkR AC ªuú]ôhPm DCªuú]ôhPUôL LmëúPhPôo (commutator)êXm DC ù_]úWhP¬p Uôt\lTÓ¡\Õ.
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T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.13.41
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