(science for class 9)

ÿ„U ¬ÈSÃ∑§ Ÿÿ ‚Ë0’Ë0∞‚0ß¸0 ∑§Ê‚¸ ∞fl¢ ŸÿË ∞Ÿ0‚Ë0ß¸0•Ê⁄U0≈UË0 ªÊß«U‹Êßã‚ ∑§ •ŸÈ‚Ê⁄U ∑§ˇÊÊ 9 ∑§ Á‹∞ ÃÒÿÊ⁄U ∑§Ë ªÿË „ÒU–

ÁflôÊÊŸ ∑§ˇÊÊ ~ ∑§ Á‹∞(Science for claSS 9)

(÷Êª-v)

÷ÊÒÁÃ∑§ ÁflôÊÊŸ(PhySicS)

‹π◊Ë⁄U Á‚¢„U∞fl¢

◊Ÿ¡ËÃ ∑§ÊÒ⁄U

ewY;ijd

iz'u

(mÙkj l

fgr)

[Value-Based Questions

(with answers)]

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© 2003, Lakhmir Singh & Manjit Kaur

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First Published in 2003Revised Edition 2014, 2016Reprints 2007, 2008, 2010, 2012, 2013, 2015, 2016

ISBN : 978-93-856-7665-9 Code : 1016C 284

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∑§ˇÊÊ 9 ∑§ ¿UÊòÊ-¿UÊòÊÊ•Ê¥ ∑§ Á‹∞

Á„UãŒË ÷Ê·Ë ˇÊòÊÊ¥, Áfl‡Ê·∑§⁄U ©UûÊ⁄U ¬˝Œ‡Ê, Á’„UÊ⁄U, ◊äÿ ¬˝Œ‡Ê, ⁄UÊ¡SÕÊŸ, ¤ÊÊ⁄Uπ¢«U ∞fl¢ ¿UûÊË‚ª…∏U, ‚ „U¡Ê⁄UÊ¥ ¿UÊòÊ-¿UÊòÊÊ•Ê¥ ∑§ ¬òÊ „U◊Ê⁄U ¬Ê‚ •Ê∞ Á∑§ Science for Class 9 Parts I, II ∞fl¢ III ¬ÈSÃ∑¥§ ¡Ê •¢ª˝¡Ë ◊¥ „U◊Ÿ ¬˝∑§ÊÁ‡ÊÃ ∑§Ë „Ò¥U fl ◊‡Ê„ÍU⁄U ‹π∑§Ê¥ üÊË ‹π◊Ë⁄U Á‚¢„U ∞fl¢ üÊË◊ÃË ◊Ÿ¡ËÃ ∑§ÊÒ⁄U Ÿ Á‹πË „Ò¥U ©UŸ∑§Ê Á„ãŒË ‚¢S∑§⁄UáÊ •Ê¬ ÄÿÊ¥ Ÿ„UË¥ ¬˝∑§ÊÁ‡ÊÃ ∑§⁄UÃ? ∑È§¿U ÁfllÊÁÕ¸ÿÊ¥ Ÿ ÃÊ ÿ„UÊ¢ Ã∑§ Á‹πÊ Á∑§ ÄÿÊ •ë¿UË ¬ÈSÃ∑§ ‚ Science ∑§fl‹ •¢ª˝¡Ë ÷Ê·Ê ◊¥ „UË ¬…∏UË ¡Ê ‚∑§ÃË „Ò? ÄÿÊ¥ Ÿ„UË¥ •Ê¬ •¢ª˝¡Ë ÷Ê·Ê flÊ‹Ë ß‚ ‚ÈãŒ⁄U ¬ÈSÃ∑§ ∑§Ê Á„ãŒË ◊¥ ¬˝∑§ÊÁ‡ÊÃ ∑§⁄UÃ „Ò¥U?

„U◊Ê⁄U Á‹∞ ¿UÊòÊÊ¥ ∑§ ÿ ¬˝‡Ÿ ¤Ê∑§¤ÊÊ⁄U ŒŸ flÊ‹ Õ– Á„UãŒË „U◊Ê⁄UË ◊ÊÃÎ÷Ê·Ê „ÒU •ÊÒ⁄U ÿ„U „U◊Ê⁄UÊ ŒÈ÷Ê¸Çÿ „ÒU Á∑§ •¬ŸË ÷Ê·Ê ◊¥ „U◊ •ë¿UË ¬ÈSÃ∑¥§ ¬˝∑§ÊÁ‡ÊÃ Ÿ„UË¥ ∑§⁄U ¬Ê ⁄U„U „Ò¥U– ÿ„U ∞∑§ øÈŸÊÒÃË ÷⁄UÊ ∑§Êÿ¸ ÕÊ– „U◊Ÿ •¬Ÿ ‹π∑§Ê¥ üÊË ‹π◊Ë⁄U Á‚¢„U ∞fl¢ üÊË◊ÃË ◊Ÿ¡ËÃ ∑§ÊÒ⁄U ‚ ’ÊÃ ∑§Ë– ©UŸ∑§Ê ∑§„UŸÊ ÕÊ Á∑§ ÁflôÊÊŸ ∑§ Á‚fÊãÃ ÃÊ ‚÷Ë ¬ÈSÃ∑§Ê¥ ◊¥ ∞∑§ ‚ „UË „UÊÃ „Ò¥U ¬⁄UãÃÈ ©Uã„¥U ¬˝SÃÈÃ ∑§⁄UŸ ∑§ …¢Uª ◊¥ ÁŸÁ‡øÃ M§¬ ‚ •ãÃ⁄U „UÊÃÊ „ÒU– ÿÁŒ ¬ÈSÃ∑§ ‚⁄U‹ Á„UãŒË ÷Ê·Ê ◊¥ Á‹πË ¡Ê∞ fl ©Ug‡ÿ ÿ„U „UÊ Á∑§ ∑§◊¡Ê⁄U ‚ ∑§◊¡Ê⁄U ÁfllÊÕË¸ ∑§Ê ÷Ë ÁflôÊÊŸ •Ê‚ÊŸË ‚ ‚◊¤Ê ◊¥ •Ê ¡Ê∞, ÃÊ ’„ÈUÃ •ë¿UÊ „UÊªÊ– ¬ÈSÃ∑§ ∑§Ê ¬…∏UÃ ‚◊ÿ ÁfllÊÕË¸ ∑§Ê ∞‚Ê •ŸÈ÷fl „UÊ Á∑§ ©U‚∑§ •äÿÊ¬∑§ ‚ÊÕ ’Ò∆U∑§⁄U Sflÿ¢ „UË ©U‚ ‚◊¤ÊÊ ⁄U„U „Ò¥U– ‹π∑§Ê¥ ∑§Ë ’ÊÃ ¬⁄U ªÊÒ⁄U ∑§⁄U „U◊Ÿ ©UŸ∑§Ë •¢ª˝¡Ë ◊¥ ÁflôÊÊŸ ∑§Ë ◊‡Ê„ÍU⁄U ¬ÈSÃ∑§Ê¥ ∑§Ê Á„UãŒË ◊¥ ¬˝∑§ÊÁ‡ÊÃ ∑§⁄UŸ ∑§Ê ÁŸ‡øÿ Á∑§ÿÊ– ¬ÈSÃ∑§Ê¥ ∑§Ê Á„UãŒË∑§⁄UáÊ ∑§⁄UŸ ∑§ Á‹∞ „U◊Ÿ ©UûÊ⁄U ÷Ê⁄UÃ ∑§ Á„UãŒË ◊¥ ÁflôÊÊŸ ¬ÈSÃ∑§Ê¥ ∑§ ¬˝Á‚f ‹π∑§ «UÊÚ. •Ê◊ ¬˝∑§Ê‡Ê ‡ÊÈÄ‹Ê, M.Sc., M.Ed., M.Phil., Ph.D., ¬˝ÊøÊÿ¸, •ÊøÊÿ¸ Ÿ⁄Uãº˝ Œfl ¬ÊS≈Uª˝¡È∞≈U ∑§ÊÚ‹¡, ‚ËÃÊ¬È⁄U (©U.¬˝.) ∑§Ê ÿ„U ŒÊÁÿàfl ‚ÊÒ¥¬Ê– «UÊÚ. ‡ÊÈÄ‹Ê Ÿ ’«∏ ⁄UÊø∑§ ∞fl¢ flÒôÊÊÁŸ∑§ …¢Uª ‚ üÊË ‹π◊Ë⁄U Á‚¢„U ∞fl¢ üÊË◊ÃË ◊Ÿ¡ËÃ ∑§ÊÒ⁄U ∑§Ë •¢ª˝¡Ë ◊¥ Á‹πË ¬ÈSÃ∑§Ê¥ ∑§Ê Á„UãŒË ÷Ê·Ê ◊¥ ¬˝SÃÈÃ Á∑§ÿÊ „ÒU–

bl iqLrd ds vUr esa ewY;ijd iz'u (mÙkj lfgr) [Value-Based Questions (with Answers)] Hkh fn;s x;s gaSA

„U◊¥ ¬ÍáÊ¸ Áfl‡flÊ‚ „ÒU Á∑§ ß‚ ¬ÈSÃ∑§ ∑§Ê ¬…∏UŸ ∑§ ’ÊŒ ÁfllÊÁÕ¸ÿÊ¥ ∑§Ê Á„UãŒË ◊¥ •ë¿UË ÁflôÊÊŸ ∑§Ë ¬ÈSÃ∑§Ê¥ ∑§Ë ¡Ê ∑§◊Ë ÕË fl„U ¬Í⁄UË „UÊªË ∞fl¢ ÁflôÊÊŸ ∑§ ¬∆UŸ-¬Ê∆UŸ ◊¥ L§Áø ©Uà¬ãŸ „UÊªË–

µ ¬˝∑§Ê‡Ê∑§

Áfl·ÿ-‚ÍøËv. ªÁÃ .................. 5&40 (Motion)

w. ’‹ ∞fl¢ ªÁÃ osQ§ ÁŸÿ◊ .................. 41&65 (Force and Laws of Motion)

x. ªÈL§àflÊ∑§·¸áÊ .................. 66&103 (Gravitation)

y. ∑§Êÿ¸ •ÊÒ⁄U ™§¡Ê¸ .................. 104&131 (Work and Energy)

z. äflÁŸ .................. 132&168 (Sound)

ewY;ijd iz'u (mÙkj lfgr) .................. 169&184 [Value-Based Questions (with answers)]

•ãÃ—flÁáÊ¸Ã

ø‹ËªÿËŒÍ⁄UË∞fl¢ÁflSÕÊ¬Ÿ ∞∑§‚◊ÊŸ∞fl¢•‚◊ÊŸªÁÃ

øÊ‹ flª

àfl⁄UáÊ ∞∑§‚◊ÊŸàflÁ⁄UÃªÁÃ∑§‚◊Ë∑§⁄UáÊ

ªÁÃ∑§Êª˝Ê»§ËÁŸM§¬áÊ ª˝Ê»§Ë¬hÁÃmÊ⁄UÊªÁÃ∑§‚◊Ë∑§⁄UáÊ√ÿÈà¬ãŸ∑§⁄UŸÊ

∞∑§‚◊ÊŸflÃÈ¸‹ªÁÃ

is«∏UU∞∑§„UËSÕÊŸ¬⁄UÁSÕÃ⁄U„UÃÊ„ÒU,ß‚Á‹∞„U◊∑§„UÃ„Ò¥UÁ∑§fl„UÁSÕ⁄U(ÿÊSÕÊŸ’h)„Ò–©U‚Ë¬˝∑§Ê⁄U,ÉÊ⁄U,S∑Í§‹,∑§Ê⁄UπÊŸÊ,ÁfllÈÃ-π¢÷•ı⁄U≈U‹Ë»§ÙŸπ¥÷,‚÷ËÁSÕ⁄UflSÃÈ∞°„Ò¥U¡Ù∞∑§„UËSÕÊŸ¬⁄UÁSÕÃ⁄U„UÃË„Ò¥U–ŒÍ‚⁄UË•Ù⁄U,◊ŸÈcÿ,¡¢ÃÈ ,¬ˇÊË,∑§Ê⁄U,’‚,⁄U‹ªÊ«∏UË,¡„UÊ¡•ı⁄UflÊÿÈÿÊŸ,ßàÿÊÁŒ,‚ê¬ÍáÊ¸‚◊ÿÁSÕ⁄UŸ„UË¥⁄U„UÃ„Ò¥U–fl∞∑§SÕÊŸ‚ŒÍ‚⁄USÕÊŸ∑§ÙªÁÃ∑§⁄U‚∑§Ã„Ò¥U–

©UŒÊ„U⁄UáÊÊÕ¸,◊ŸÈcÿªÁÃ∑§⁄UÃÊ„ÒU,¡’fl„U‚«∏U∑§∑§Á∑§ŸÊ⁄U-Á∑§ŸÊ⁄Uø‹ÃÊ„ÒU,¬ˇÊËªÁÃ∑§⁄UÃÊ„ÒU¡’fl„U•Ê∑§Ê‡Ê◊¥©U«∏UÃÊ„ÒU,•ı⁄U◊¿U‹ËªÁÃ∑§⁄UÃË„ÒU¡’fl„U¡‹◊¥ÃÒ⁄UÃË„ÒU–©U‚Ë¬˝∑§Ê⁄U,∑§Ê⁄U•ÕflÊ’‚‚«∏U∑§¬⁄UªÁÃ∑§⁄UÃË„ÒU,⁄U‹ªÊ«∏UË⁄U‹¬Õ¬⁄UªÁÃ∑§⁄UÃË„ÒU,¡„UÊ¡¡‹◊¥ªÁÃ∑§⁄UÃÊ„ÒU•ı⁄UflÊÿÈÿÊŸªÁÃ∑§⁄UÃÊ„ÒU¡’fl„U∞∑§SÕÊŸ‚ŒÍ‚⁄USÕÊŸ∑§ÙflÊÿÈ◊¥©U«∏UÃÊ„ÒU–Á∑§‚ËÁ¬¢«U(•ÕflÊflSÃÈ)∑§Ê‚¢ø‹Ÿ,ªÁÃ∑§„U‹ÊÃÊ„ÒU–‚÷Ë ªÁÃ◊ÊŸ Á¬¢«UÙ¥ (•ÕflÊ flSÃÈ•Ù¥) ∑§Ê ∞∑§ ‚Ê◊Êãÿ ‹ˇÊáÊ „UÙÃÊ „ÒU Á∑§ fl ‚◊ÿ ∑§ ‚ÊÕ •¬ŸË ÁSÕÁÃ ’Œ‹Ã „Ò¥U– „U◊ªÁÃ∑§Ù•’ÁŸêŸ¬˝∑§Ê⁄U¬Á⁄U÷ÊÁ·Ã∑§⁄U‚∑§Ã„Ò¥U—

Á∑§‚Ë Á¬¢«U (•ÕflÊ flSÃÈ) ∑§Ù ªÁÃ ◊¥ (•ÕflÊ ªÁÃ‡ÊË‹) ∑§„UÊ ¡ÊÃÊ „ÒU ¡’ ©U‚∑§Ë ÁSÕÁÃ Á∑§‚Ë ÁSÕ⁄U flSÃÈ ∑§ ‚¢Œ÷¸ ◊¥ ‹ªÊÃÊ⁄U ’Œ‹ÃË „ÒU– ©UŒÊ„U⁄UáÊÊÕ¸,∑§Ê⁄U∑§ËÁSÕÁÃ¡’ÉÊ⁄UÙ¥•ı⁄U¬«∏UÙ¥ßàÿÊÁŒ,¡Ò‚ËÁSÕ⁄UflSÃÈ•Ù¥∑§‚¢Œ÷¸◊¥‹ªÊÃÊ⁄U’Œ‹ÃË„ÒU,„U◊∑§„UÃ„Ò¥UÁ∑§∑§Ê⁄Uø‹⁄U„UË„ÒU•ÕflÊÁ∑§∑§Ê⁄UªÁÃ◊¥„ÒU–ªÁÃ∑§•Õ¸∑§Ù•Áœ∑§S¬CÔUM§¬‚‚◊¤ÊŸ∑§Á‹∞„U◊∞∑§©UŒÊ„U⁄UáÊ‹Ã„Ò¥U–

fLFkj oLrq,¡

xfr'khy dkj

ik¡p lsd.M osQ ckn dkj ;gk¡ igq¡prh gSA

?kj

isM+

ÁøòÊ v. ‚◊ÿ∑§‚ÊÕªÁÃ‡ÊË‹∑§Ê⁄U∑§ËÁSÕÁÃ’Œ‹ÃË„ÒU–ß‚Á‹∞,∑§Ê⁄UªÁÃ◊¥„UÙÃË„ÒU–

5

ªÁÃ(Motion)

1

∞∑§Áfl‡Ê·‚◊ÿ¬⁄U,¬«∏U•ı⁄UÉÊ⁄U∑§‚Ê◊ŸÁSÕÁÃA¬⁄UÁøòÊv◊¥„U◊∞∑§∑§Ê⁄UŒπÃ„Ò¥U(ß‚∑§‚◊¥,ÉÊ⁄U•ı⁄U¬«∏UÁSÕ⁄UflSÃÈ∞°„Ò¥UÁ¡ã„¥U‚¢Œ÷¸Á’¢ŒÈ∑§M§¬◊¥Á‹ÿÊªÿÊ„ÒU)–•’,z‚∑§á«U’ÊŒ,„U◊©U‚Ë∑§Ê⁄U∑§ÙÁSÕÁÃB¬⁄UŒπÃ„Ò¥U¡ÙÉÊ⁄U•ı⁄U¬«∏U‚∑§Ê»§ËŒÍ⁄U„ÒU(Œπ¥ÁøòÊv)–ß‚∑§Ê•Õ¸„ÒUÁ∑§ÁSÕ⁄UflSÃÈ,ÉÊ⁄U•ÕflÊ¬«∏U∑§‚¢Œ÷¸◊¥,ß‚∑§Ê⁄U∑§ËÁSÕÁÃ‹ªÊÃÊ⁄U’Œ‹⁄U„UË„ÒU–ß‚Á‹∞,„U◊∑§„UÃ„Ò¥UÁ∑§ÿ„U∑§Ê⁄Uø‹⁄U„UË„ÒU•ÕflÊÁ∑§ÿ„U∑§Ê⁄UªÁÃ◊¥„ÒU–„U◊Ê⁄UøÊ⁄UÙ¥•Ù⁄U∑È§¿U•ãÿÁ¬á«U(•ÕflÊflSÃÈ∞°)„Ò¥U,¡ÙªÁÃ∑§ÁflÁ÷ãŸ¬˝∑§Ê⁄UÙ¥∑§ÙŒ‡ÊÊ¸ÃË„Ò¥U—¤ÊÍ‹Ê,◊⁄UË-ªÙ-⁄UÊ©¢U«U,ŒËflÊ‹ÉÊ«∏UË∑§Ê‹Ù‹∑§,ÃÕÊÉÊ«∏UË∑§Ë‚ÈßÿÊ°–

ÿÁŒ ∑§Ùß¸ Á¬á«U (•ÕflÊ flSÃÈ) ¬ÿÊ¸# ÃËfl˝ ªÁÃ ∑§⁄UÃÊ „ÒU, ÃÙ ©U‚∑§ ‚¢ø‹Ÿ (•ÕflÊ ªÁÃ) ∑§Ù •Ê‚ÊŸË ‚ ŒπÊ ¡Ê ‚∑§ÃÊ „ÒU– ¬⁄UãÃÈ ÿÁŒ Á¬á«U •àÿÁœ∑§ ◊¢Œ ªÁÃ ∑§⁄UÃÊ „ÒU ÃÙ ©U‚∑§ ‚¢ø‹Ÿ ∑§Ù Ãà∑§Ê‹ ŒπŸÊ ∑§Á∆UŸ „UÙÃÊ „ÒU– ©UŒÊ„U⁄UáÊÊÕ¸,∑§‹Êß¸ÉÊ«∏UË◊¥ÃËŸ‚ÈßÿÊ°„UÙÃË„Ò¥U—‚∑§á«UflÊ‹Ë‚Èß¸,Á◊Ÿ≈UflÊ‹Ë‚Èß¸,•ı⁄UÉÊá≈UflÊ‹Ë‚Èß¸,¡ÙÉÊ«∏UË∑§«UÊÿ‹¬⁄UªÙ‹Êß¸◊¥ªÁÃ∑§⁄UÃË„Ò¥U–•’,ÉÊ«∏UË∑§Ë‚∑§á«UflÊ‹Ë‚Èß¸∑§Ê»§ËÃ¡ªÁÃ∑§⁄UÃË„ÒU,ß‚Á‹∞„U◊ÉÊ«∏UË∑§‚∑§á«UflÊ‹Ë‚Èß¸∑§ËªÁÃ∑§Ù∑§Ê»§Ë•Ê‚ÊŸË‚Œπ‚∑§Ã„Ò¥U–¬⁄UãÃÈÉÊ«∏UË∑§ËÁ◊Ÿ≈UflÊ‹Ë‚Èß¸•ı⁄UÉÊá≈UflÊ‹Ë‚Èß¸∑§Ê»§ËœË⁄Uø‹ÃË„Ò¥U,ß‚Á‹∞©UŸ∑§ËªÁÃ∑§Ù•Ê‚ÊŸË‚Ÿ„UË¥ŒπÊ¡Ê‚∑§ÃÊ„ÒU–ÿ„U¬ÃÊ‹ªÊŸ∑§Á‹∞Á∑§Á◊Ÿ≈UflÊ‹Ë‚Èß¸•ı⁄UÉÊá≈UflÊ‹Ë‚Èß¸ø‹⁄U„UË„ÒU•ÕflÊŸ„UË¥,„U◊¥©UŸ∑§ËÁSÕÁÃ∑§Ù¬ÿÊ¸#‚◊ÿÃ∑§ŒπÃ⁄U„UŸÊ„UÙªÊ–∑§Ê⁄UáÊÿ„U„ÒU,¡’∑§Ùß¸flSÃÈªÁÃ∑§⁄UÃË„ÒU,‚◊ÿ∑§‚ÊÕ©U‚∑§ËÁSÕÁÃ’Œ‹ÃË„ÒU–

Á¬á«UÙ¥(•ÕflÊflSÃÈ•Ù¥)∑§ËªÁÃ∑§Ê•äÿÿŸ∑§⁄UŸ∑§Á‹∞,„U◊¥¬„U‹ŒÙ‡ÊéŒÙ¥—ŒÍ⁄UË (distance)•ı⁄UÁflSÕÊ¬Ÿ (displacement)∑§Ê•Õ¸¡ÊŸ‹ŸÊøÊÁ„U∞–ßŸ∑§Ë¬Á⁄UøøÊ¸ŸËø∑§ËªÿË„ÒU–∞∑§•ı⁄U’ÊÃŸÙ≈U∑§⁄UŸ∑§Ë„ÒUÁ∑§ªÁÃ∑§•äÿÿŸ◊¥,„U◊øÊ„U‡ÊéŒ“Á¬á«U”(body) •ÕflÊ“flSÃÈ”(object)∑§Ê©U¬ÿÙª∑§⁄¥U,ŒÙŸÙ¥∑§Ê•Õ¸∞∑§„UË„ÒU–

ø‹Ë ªÿË ŒÍ⁄UË ∞fl¢ ÁflSÕÊ¬Ÿ (DiStAnCE tRAVELLED AnD DiSPLACEMEnt)

¬˝ÁÃÁŒŸ∑§Ë÷Ê·Ê◊¥,‡ÊéŒŒÍ⁄UË(distance)•ı⁄U ÁflSÕÊ¬Ÿ(displacement)∞∑§„UË•Õ¸◊¥¬˝ÿÙªÁ∑§ÿ¡ÊÃ„Ò¥U¬⁄UãÃÈ÷ıÁÃ∑§Ë◊¥ßŸŒÙŸÙ¥‡ÊéŒÙ¥∑§Á÷ãŸ-Á÷ãŸ•Õ¸„UÙÃ„Ò¥U–„U◊∞∑§©UŒÊ„U⁄UáÊ‹∑§⁄Uß‚•¢Ã⁄U∑§Ù‚◊¤ÊÃ„Ò¥U–

◊ÊŸÊÁ∑§∑§Ùß¸√ÿÁQ§SÕÊŸA¬⁄U⁄U„UÃÊ„ÒU(ÁøòÊw)•ı⁄U©U‚∞∑§•ãÿSÕÊŸC¬⁄U¬„È°UøŸÊ„ÒU,¬⁄UãÃÈ¬„U‹©U‚SÕÊŸB¬⁄U⁄U„UŸflÊ‹•¬ŸÁ◊òÊ‚Á◊‹ŸÊ„ÒU–•’,√ÿÁQ§Á’¢ŒÈA‚ø‹ŸÊ•Ê⁄Uê÷∑§⁄UÃÊ„ÒU•ı⁄UBÃ∑§¬„È°UøŸ∑§Á‹∞zÁ∑§◊Ë∑§ËŒÍ⁄UËÃÿ∑§⁄UÃÊ„ÒU,•ı⁄Uß‚∑§’ÊŒB‚CÃ∑§¬„È°UøŸ∑§Á‹∞xÁ∑§◊Ë∑§Ë•ı⁄UŒÍ⁄UËÃÿ∑§⁄UÃÊ„ÒU–ß‚¬˝∑§Ê⁄U,√ÿÁQ§◊Êª¸ABC∑§‚„UÊ⁄U(Á’¢ŒÈŒÊ⁄U⁄UπÊ•Ù¥mÊ⁄UÊŒ‡ÊÊ¸ÿÊªÿÊ)ø‹ÃÊ„ÒU–◊Êª¸ABC∑§Ë‹ê’Êß¸√ÿÁQ§mÊ⁄UÊø‹ËªÿËflÊSÃÁfl∑§ŒÍ⁄UË∑§Ù’ÃÊÃÊ„ÒU–•Ã—,flSÃÈ mÊ⁄UÊ ø‹Ë ªÿË ŒÍ⁄UË, ÁŒ‡ÊÊ Á¡‚◊¥ flSÃÈ ø‹ÃË „ÒU, ∑§Ë ¬⁄UflÊ„U Á∑§ÿ Á’ŸÊ ªÁÃ‡ÊË‹ flSÃÈ mÊ⁄UÊ Ãÿ Á∑§ÿ ªÿ ◊Êª¸ ∑§Ë flÊSÃÁfl∑§ ‹ê’Êß¸ „UÙÃË „ÒU– ©UŒÊ„U⁄UáÊÊÕ¸,ß‚ÁSÕÁÃ◊¥,√ÿÁQ§mÊ⁄UÊÃÿÁ∑§ÿªÿflÊSÃÁfl∑§◊Êª¸∑§Ë‹ê’Êß¸zÁ∑§◊Ë+xÁ∑§◊Ë=}Á∑§◊Ë„ÒU,ß‚Á‹∞√ÿÁQ§mÊ⁄UÊø‹ËªÿËŒÍ⁄UË}Á∑§◊Ë„ÒU–

„U◊•’ß‚‚◊SÿÊ¬⁄UŒÍ‚⁄UËÃ⁄U„U‚ÁfløÊ⁄U∑§⁄¥Uª–¡’√ÿÁQ§Á’¢ŒÈC¬⁄U¬„È°UøÃÊ„ÒU,„U◊¡ÊŸŸÊøÊ„UÃ„Ò¥UÁ∑§fl„U¬˝Ê⁄Uê÷∑§Á’¢ŒÈA‚Á∑§ÃŸËŒÍ⁄U„ÒU,•ÕÊ¸Ã˜,„U◊Á’¢ŒÈA•ı⁄UÁ’¢ŒÈC∑§’Ëø‚’‚∑§◊ŒÍ⁄UË¡ÊŸŸÊøÊ„UÃ„Ò¥U–„U◊A•ı⁄UC∑§’Ëø∞∑§‚ËœË⁄UπÊACπË¥øÃ„Ò¥U–‚ËœË⁄UπÊAC◊Êª¸∑§Ë‹ê’Êß¸(¡Ùÿ„UÊ°¬⁄UyÁ∑§◊Ë„ÒU)Á’¢ŒÈA‚√ÿÁQ§∑§ÊÁflSÕÊ¬Ÿ„ÒU,•ÕÊ¸Ã˜ ,C¬⁄U¬„È°UøŸ¬⁄U,√ÿÁQ§¬˝Ê⁄Uê÷Á’¢ŒÈA‚∑§fl‹yÁ∑§◊ËŒÍ⁄U„ÒU–ÿ„UÁflSÕÊ¬Ÿ¬Ífl¸ÁŒ‡ÊÊ◊¥„ÒU–•Ã—,¡’ ∞∑§ flSÃÈ ∞∑§ Á’¢ŒÈ ‚ ŒÍ‚⁄U Á’ãŒÈ ∑§Ë •Ù⁄U ø‹ÃË „ÒU, ø‹Ë ªÿË ŒÍ⁄UË •¬˝àÿˇÊ ◊Êª¸ ∑§Ë flÊSÃÁfl∑§ ‹ê’Êß¸ ’Ã‹ÊÃË „ÒU ¡’Á∑§ ÁflSÕÊ¬Ÿ, ¬˝Ê⁄UÁê÷∑§ •ı⁄U •¢ÁÃ◊ ÁSÕÁÃÿÙ¥ ∑§ ’Ëø ‚ËœË ⁄UπÊ ◊Êª¸ ∑§Ù ’Ã‹ÊÃÊ „ÒU– ß‚Á‹∞,ªÁÃ‡ÊË‹flSÃÈmÊ⁄UÊø‹ËªÿËŒÍ⁄UË¡Ù÷Ë„UÙ,flSÃÈ∑§ÊÁflSÕÊ¬Ÿ‚ŒÒflflSÃÈ∑§Ë¬˝Ê⁄UÁê÷∑§•ı⁄U•¢ÁÃ◊ÁSÕÁÃÿÙ¥∑§’Ëø‚’‚∑§◊ŒÍ⁄UËmÊ⁄UÊ¬˝ŒÁ‡Ê¸ÃÁ∑§ÿÊ¡ÊÃÊ„ÒU–•Ã—,flSÃÈ ¡’ ∞∑§ ÁSÕÁÃ ‚ ŒÍ‚⁄UË ÁSÕÁÃ Ã∑§ ø‹ÃË „ÒU, ÁŒ‡ÊÊ ∑§ ‚ÊÕ, flSÃÈ ∑§Ë ¬˝Ê⁄UÁê÷∑§ ÁSÕÁÃ •ı⁄U •¢ÁÃ◊ ÁSÕÁÃ ∑§ ’Ëø ‚’‚ ¿UÙ≈UË (‚ËœË ⁄UπÊ) ŒÍ⁄UË ©U‚∑§ ÁflSÕÊ¬Ÿ ∑§ M§¬ ◊¥ ¡ÊŸË ¡ÊÃË „ÒU–

©U¬ÿÈ¸ÄÃ©UŒÊ„U⁄UáÊ◊¥,√ÿÁQ§∑§Ë¬˝Ê⁄UÁê÷∑§ÁSÕÁÃA•ı⁄U•¢ÁÃ◊ÁSÕÁÃC∑§’Ëø‚’‚¿UÙ≈UËŒÍ⁄UËyÁ∑§◊Ë„ÒU,ß‚Á‹∞¬Ífl¸ÁŒ‡ÊÊ◊¥√ÿÁQ§∑§ÊÁflSÕÊ¬ŸyÁ∑§◊Ë„ÒU–ÿ„US¬CÔU„ÒUÁ∑§ø‹Ë ªÿË ŒÍ⁄UË ◊¥ ∑§fl‹ ¬Á⁄U◊ÊáÊ (magnitude)„UÙÃÊ „ÒU, ¡’Á∑§ ÁflSÕÊ¬Ÿ ◊¥ ¬Á⁄U◊ÊáÊ ∑§ ‚ÊÕ-‚ÊÕ ÁŒ‡ÊÊ ÷Ë „UÙÃË „ÒU–

ŒÍ⁄UË,ÁflSÕÊ¬Ÿ,ßàÿÊÁŒ,¡Ò‚Ë⁄UÊÁ‡ÊÿÊ°÷ıÁÃ∑§⁄UÊÁ‡ÊÿÊ°(•ÕflÊ÷ıÁÃ∑§Ë∑§Ë⁄UÊÁ‡ÊÿÊ°)∑§„UË¡ÊÃË„Ò¥U–÷ıÁÃ∑§⁄UÊÁ‡Ê∑§¬Á⁄U◊ÊáÊ∑§Ê•Õ¸÷ıÁÃ∑§⁄UÊÁ‡Ê∑§Ê•Ê◊Ê¬(size)„UÙÃÊ„ÒU–∑§fl‹¬Á⁄U◊ÊáÊ(•ÕflÊ•Ê◊Ê¬)ÿÈQ§÷ıÁÃ∑§⁄UÊÁ‡Ê,•ÁŒ‡Ê⁄UÊÁ‡Ê(scalar quantity)∑§„UË¡ÊÃË„ÒU–•ÁŒ‡Ê⁄UÊÁ‡Ê◊¥∑§Ùß¸ÁŒ‡ÊÊŸ„UË¥„UÙÃË„ÒU–ŒÍ‚⁄UË•Ù⁄U,¬Á⁄U◊ÊáÊ∑§‚ÊÕ-‚ÊÕÁŒ‡ÊÊÿÈQ§÷ıÁÃ∑§⁄UÊÁ‡Ê,‚ÁŒ‡Ê⁄UÊÁ‡Ê(vector quantity)∑§„UË¡ÊÃË„ÒU–

ÁøòÊ w.ø‹ËªÿËŒÍ⁄UË=z+x=}Á∑§◊ËÁflSÕÊ¬Ÿ=yÁ∑§◊Ë¬Ífl¸∑§Ë•Ù⁄U

6 HkkSfrd foKku µ iX

(i) ŒÍ⁄UË ∞∑§ •ÁŒ‡Ê ⁄UÊÁ‡Ê(scalar quantity)„ÒU(ÄÿÙ¥Á∑§ß‚◊¥∑§fl‹¬Á⁄U◊ÊáÊ„UÙÃÊ„ÒU,ß‚◊¥∑§Ùß¸ÁflÁ‡ÊCÔUÁŒ‡ÊÊŸ„UË¥„UÙÃË„ÒU)– (ii) ÁflSÕÊ¬Ÿ ∞∑§ ‚ÁŒ‡Ê ⁄UÊÁ‡Ê(vector quantity)„ÒU(ÄÿÙ¥Á∑§ß‚◊¥¬Á⁄U◊ÊáÊ∑§‚ÊÕ-‚ÊÕÁŒ‡ÊÊ÷Ë„UÙÃË„ÒU)–

©UŒÊ„U⁄UáÊÊÕ¸,ÿÁŒ∑§Ê⁄UzÆÁ∑§◊Ë∑§ËŒÍ⁄UËø‹ÃË„ÒUÃÙ√ÿ¢¡∑§ “zÆ Á∑§◊Ë” ø‹Ë ªÿË ŒÍ⁄UË „ÒU, •ı⁄UÿÁŒ∑§Ê⁄U¬Ífl¸ÁŒ‡ÊÊ◊¥(•ÕflÊÁ∑§‚Ë•ãÿÁŒ‡ÊÊ◊¥)‚ËœË⁄UπÊ◊¥ø‹⁄U„UË„ÒU,ÃÙ√ÿ¢¡∑§ “zÆ Á∑§◊Ë ¬Ífl¸ ∑§Ë •Ù⁄U” ∑§Ê⁄U ∑§Ê ÁflSÕÊ¬Ÿ „ÒU–

ªÁÃ‡ÊË‹ flSÃÈ mÊ⁄UÊ ø‹Ë ªÿË ŒÍ⁄UË ‡ÊÍãÿ Ÿ„UË¥ „UÙ ‚∑§ÃË „ÒU, ¬⁄UãÃÈ ªÁÃ‡ÊË‹ flSÃÈ ∑§Ê •¢ÁÃ◊ ÁflSÕÊ¬Ÿ ‡ÊÍãÿ „UÙ ‚∑§ÃÊ „ÒU– ªÁÃ‡ÊË‹flSÃÈ∑§ÊÁflSÕÊ¬Ÿ‡ÊÍãÿ„UÙªÊÿÁŒ,∞∑§ÁŸÁ‡øÃŒÍ⁄UËø‹Ÿ∑§’ÊŒ,ªÁÃ‡ÊË‹flSÃÈ•¢ÃÃ—•¬Ÿ¬˝Ê⁄UÁê÷∑§Á’¢ŒÈ(•ÕflÊ¬˝Ê⁄UÁê÷∑§ÁSÕÁÃ)¬⁄UflÊ¬‚•Ê¡ÊÃË„ÒU–ÿ„UÁŸêŸÁ‹ÁπÃ©UŒÊ„U⁄UáÊÙ¥‚S¬CÔU„UÙ¡ÊÿªÊ–◊ÊŸ‹¥Á∑§∞∑§√ÿÁQ§SÕÊŸA‚ø‹ÃÊ„ÒU•ı⁄USÕÊŸBÃ∑§¬„È°UøŸ◊¥zÁ∑§◊ËŒÍ⁄UËÃÿ∑§⁄UÃÊ„ÒU[Œπ¥ÁøòÊx(a)]–SÕÊŸB‚fl„UxÁ∑§◊Ë•ı⁄UŒÍ⁄UËÃÿ∑§⁄UÃÊ„ÒUÃÕÊSÕÊŸC¬⁄U¬„È°UøÃÊ„ÒU–•ı⁄U•¢ÃÃ—√ÿÁQ§¬˝Ê⁄UÁê÷∑§Á’¢ŒÈAÃ∑§flÊ¬‚¬„È°UøŸ∑§Á‹∞SÕÊŸC‚yÁ∑§◊Ëø‹ÃÊ„ÒU[Œπ¥ÁøòÊx(a)]–ß‚∑§‚◊¥,ÿlÁ¬√ÿÁQ§ŸzÁ∑§◊Ë+xÁ∑§◊Ë+yÁ∑§◊Ë=vwÁ∑§◊ËŒÍ⁄UËÃÿ∑§Ë„ÒU,¬⁄UãÃÈ√ÿÁQ§∑§Ê•ÁãÃ◊ÁflSÕÊ¬Ÿ‡ÊÍãÿ„ÒU–∑§Ê⁄UáÊÿ„U„ÒUÁ∑§√ÿÁQ§¬˝Ê⁄UÁê÷∑§Á’¢ŒÈA¬⁄U¬ÈŸ—¬„È°Uø¡ÊÃÊ„ÒUÃÕÊ¬˝Ê⁄UÁê÷∑§ÁSÕÁÃA•ı⁄U•¢ÁÃ◊ÁSÕÁÃA∑§’Ëø‚ËœË⁄UπÊŒÍ⁄UË‡ÊÍãÿ„ÒU–•Ã—,ÿÁŒ „U◊ ª◊ŸÊª◊Ÿ ∑§⁄UÃ „Ò¥U •ı⁄U ¬˝Ê⁄UÁê÷∑§ Á’¢ŒÈ ¬⁄U ¬„È°Uø ¡ÊÃ „Ò¥U ÃÙ, ÿlÁ¬ „U◊ ∑È§¿U ŒÍ⁄UË ø‹Ã „Ò¥U, „U◊Ê⁄UÊ •¢ÁÃ◊ ÁflSÕÊ¬Ÿ ‡ÊÍãÿ „UÙªÊ– ∑§Ê⁄UáÊ ÿ„U „ÒU Á∑§ ¬˝Ê⁄UÁê÷∑§ •ı⁄U •¢ÁÃ◊ ÁSÕÁÃÿÙ¥ ∑§ ’Ëø ‚ËœË ⁄UπÊ ŒÍ⁄UË ‡ÊÍãÿ „UÙªË– ©UŒÊ„U⁄UáÊÊÕ¸,ÿÁŒ„U◊ÁòÊÖÿÊr∑§ªÙ‹Ëÿ¬Õ∑§‚ÊÕ-‚ÊÕø‹Ã„Ò¥U•ı⁄U¬ÈŸ—¬˝Ê⁄UÁê÷∑§Á’¢ŒÈA¬⁄U¬„È°Uø¡ÊÃ„Ò¥U[Œπ¥ÁøòÊx(b)],ÃÙÿlÁ¬„U◊ŒÍ⁄UËwπr(¬Õ∑§Ë¬Á⁄UÁœ∑§’⁄UÊ’⁄U)ø‹Ã„Ò¥U¬⁄UãÃÈ„U◊Ê⁄UÊ•¢ÁÃ◊ÁflSÕÊ¬Ÿ‡ÊÍãÿ„UÙªÊ–„U◊•’ŒÍ⁄UË∞fl¢ÁflSÕÊ¬Ÿ¬⁄U•ÊœÊÁ⁄UÃ∞∑§‚◊SÿÊ„U‹∑§⁄¥Uª–

ÁøòÊ x. ŒÙ©UŒÊ„U⁄UáÊ¡„UÊ°flSÃÈ∞∑§ÁŸÁ‡øÃŒÍ⁄UËø‹ÃË„ÒU¬⁄UãÃÈflSÃÈ∑§Ê•¢ÁÃ◊ÁflSÕÊ¬Ÿ‡ÊÍãÿ„ÒU–

(a)ÿ„UÊ°—ø‹ËªÿËŒÍ⁄UË(A ‚A Ã∑§)=zÁ∑§◊Ë+xÁ∑§◊Ë+yÁ∑§◊Ë=vwÁ∑§◊Ë

ÁflSÕÊ¬Ÿ(A ‚A Ã∑§)=Æ

(b)ÿ„UÊ°—ø‹ËªÿËŒÍ⁄UË(A ‚A Ã∑§)=wπr(¡„UÊ°rªÙ‹Ëÿ¬Õ∑§ËÁòÊÖÿÊ„ÒU)

ÁflSÕÊ¬Ÿ(A ‚A Ã∑§)=Æ

Ÿ◊ÍŸÊÕ¸ ‚◊SÿÊ — ∞∑§√ÿÁQ§¬Ífl¸∑§Ë•Ù⁄Uv.z◊Ë,Á»§⁄UŒÁˇÊáÊ∑§Ë•Ù⁄Uw.Æ◊Ë•ı⁄U•¢ÃÃ—¬Ífl¸∑§Ë•Ù⁄Uy.z◊Ë∑§ËŒÍ⁄UËÃÿ∑§⁄UÃÊ„ÒU– (i) ø‹ËªÿË∑È§‹ŒÍ⁄UËÄÿÊ„ÒU? (ii) ©U‚∑§Ê¬Á⁄UáÊÊ◊ËÁflSÕÊ¬ŸÄÿÊ„ÒU?

„U‹ — (i)ø‹ËªÿË∑È§‹ŒÍ⁄UË=v.z+w.Æ+y.z=}.Æ◊Ë(ii)¬Á⁄UáÊÊ◊ËÁflSÕÊ¬ŸôÊÊÃ∑§⁄UŸ∑§Á‹∞,„U◊‚ÈÁflœÊ¡Ÿ∑§¬Ò◊ÊŸÊ‹∑§⁄U√ÿÁQ§∑§Ë

øÊ‹Ù¥∑§Ê◊ÊŸÁøòÊπË¥ø¥ª–◊ÊŸ‹¥Á∑§v‚◊Ë,v◊Ë∑§ÙŒ‡ÊÊÃÊ„ÒU–ÃÙ,v.z◊Ë∑§Ùv.z‚◊Ë‹ê’Ë⁄UπÊmÊ⁄UÊ,w.Æ◊Ë∑§Ùw.Æ‚◊Ë⁄UπÊmÊ⁄UÊ•ı⁄Uy.z◊Ë∑§Ùy.z‚◊Ë‹ê’Ë⁄UπÊmÊ⁄UÊŒ‡ÊÊÿÊ¡Ê‚∑§ÃÊ„ÒU–

„U◊¬Ífl¸∑§Ë•Ù⁄Uv.z◊ËŒ‡ÊÊ¸Ÿ∑§Á‹∞,¬Á‡ø◊‚¬Ífl¸∑§Ë•Ù⁄Uv.z‚◊Ë‹ê’Ë⁄UπÊABπË¥øÃ„Ò¥U(Œπ¥ÁøòÊy)–Á»§⁄UŒÁˇÊáÊ∑§Ë•Ù⁄Uw◊Ë¬˝ŒÁ‡Ê¸Ã∑§⁄UŸ∑§Á‹∞„U◊w‚◊Ë‹ê’Ë⁄UπÊBCŒÁˇÊáÊ∑§Ë•Ù⁄UπË¥øÃ„Ò¥U–•ı⁄U•ãÃ◊¥¬Ífl¸∑§Ë•Ù⁄Uy.z◊Ë∑§ËŒÍ⁄UË∑§Ù¬˝ŒÁ‡Ê¸Ã∑§⁄UŸ∑§Á‹∞¬Ífl¸∑§Ë•Ù⁄Uy.z‚◊Ë‹ê’ËÃË‚⁄UË⁄UπÊCDπË¥øÃ„Ò¥U–•’,¬˝Ê⁄UÁê÷∑§Á’¢ŒÈA∑§‚ÊÕ•¢ÁÃ◊Á’¢ŒÈD∑§ÙÁ◊‹Ê∑§⁄U,¬Á⁄UáÊÊ◊ËÁflSÕÊ¬Ÿ¬˝Ê#Á∑§ÿÊ¡Ê‚∑§ÃÊ„ÒU–•Ã—⁄UπÊCD√ÿÁQ§∑§•¢ÁÃ◊ÁflSÕÊ¬Ÿ∑§Ù¬˝ŒÁ‡Ê¸Ã∑§⁄UÃÊ„ÒU–„U◊⁄UπÊAD∑§Ë‹ê’Êß¸◊Ê¬Ã„Ò¥U–ÿ„U{.x‚◊Ë¬˝Ê#„UÙÃË„ÒU–

•’, v‚◊Ë=v◊Ë ß‚Á‹∞ ,{.x‚◊Ë={.x◊Ë•Ã—¡Ò‚ÊÁ∑§ADmÊ⁄UÊ¬˝ŒÁ‡Ê¸Ã„UÙÃÊ„ÒU,¬Á⁄UáÊÊ◊ËÁflSÕÊ¬Ÿ{.x◊Ë„ÒU–

ÁøòÊ y. Ÿ◊ÍŸÊÕ¸‚◊SÿÊ∑§Á‹∞⁄UπÊÁøòÊ(¬Ò◊ÊŸÊ—v‚◊Ë=v◊Ë)

xfr 7

∑Î§¬ÿÊŸÙ≈U∑§⁄¥UÁ∑§¡’ ∑§Ùß¸ flSÃÈ •Ê«∏U-ÁÃ⁄U¿U ◊Êª¸ ¬⁄U ø‹ÃË „ÒU, •¢ÁÃ◊ ÁflSÕÊ¬Ÿ, flSÃÈ ∑§ ¬˝Ê⁄UÁê÷∑§ Á’¢ŒÈ •ı⁄U •¢ÁÃ◊ Á’¢ŒÈ ∑§Ù ‚ËœË ⁄UπÊ ‚ ¡Ù«∏UŸ ¬⁄U ¬˝Ê# „UÙÃÊ „ÒU– „U◊•’ÁŸêŸÁ‹ÁπÃ¬˝‡ŸÙ¥∑§©UûÊ⁄UŒŸ∑§ËÁSÕÁÃ◊¥„Ò¥U— v. ÄÿÊÁflSÕÊ¬Ÿ∞∑§•ÁŒ‡Ê⁄UÊÁ‡Ê„ÒU? w. ∞∑§flSÃÈÁòÊÖÿÊR∑§flÎûÊËÿ◊Êª¸¬⁄UªÁÃ∑§⁄U⁄U„UË„ÒU–¡’fl„U•ÊœÊ¬Á⁄U∑˝§◊áÊ¬Í⁄UÊ∑§⁄U‹ÃË„ÒUÃÙflSÃÈ∑§Ëø‹ËªÿËŒÍ⁄UË•ı⁄U

ÁflSÕÊ¬ŸÄÿÊ„UÙªÊ? x. ÁŸêŸÁ‹ÁπÃ◊¥©U¬ÿÈQ§‡ÊéŒÙ¥‚Á⁄UQ§SÕÊŸÙ¥∑§Ë¬ÍÁÃ¸∑§ËÁ¡∞— ÁflSÕÊ¬Ÿ∞∑§................⁄UÊÁ‡Ê„ÒU¡’Á∑§ŒÍ⁄UË∞∑§................⁄UÊÁ‡Ê„ÒU– y. flSÃÈmÊ⁄UÊ“ø‹ËªÿËŒÍ⁄UË”•ı⁄U©U‚∑§“ÁflSÕÊ¬Ÿ”◊¥ÄÿÊ•¢Ã⁄U„ÒU?⁄UπÊÁøòÊ∑§Ë‚„UÊÿÃÊ‚‚◊¤ÊÊßÿ– z. ’ÃÊßÿÁ∑§ŒÍ⁄UË∞∑§•ÁŒ‡Ê⁄UÊÁ‡Ê„ÒU•ÕflÊ‚ÁŒ‡Ê⁄UÊÁ‡Ê„ÒU? {. ÿÁŒ•Ê¬ª◊ŸÊ-ª◊Ÿ»§⁄U◊¥{Á∑§◊Ëø‹Ã„Ò¥U•ı⁄UÁ»§⁄UflÊ¬‚ÉÊ⁄U•ÊÃ„Ò¥U— (•) •Ê¬ŸÁ∑§ÃŸËŒÍ⁄UËø‹Ë„ÒU? (’)•Ê¬∑§Ê•¢ÁÃ◊ÁflSÕÊ¬ŸÄÿÊ„ÒU? |. ªÁÃ∑§Ù¬Á⁄U÷ÊÁ·Ã∑§ËÁ¡∞– }. Á∑§Ÿ¬Á⁄UÁSÕÁÃÿÙ¥◊¥∑§Ùß¸flSÃÈÁŸÁ‡øÃŒÍ⁄UËÃ∑§ø‹‚∑§ÃË„ÒU•ı⁄UÁ»§⁄U÷Ë©U‚∑§Ê¬Á⁄UáÊÊ◊ËÁflSÕÊ¬Ÿ‡ÊÍãÿ⁄U„UÃÊ„ÒU? ~. ∞∑§flSÃÈ¬Ífl¸∑§Ë•Ù⁄UxÁ∑§◊ËŒÍ⁄UËÃ∑§ø‹ÃË„ÒU,Á»§⁄U©UûÊ⁄U∑§Ë•Ù⁄UyÁ∑§◊Ëø‹ÃË„ÒU•ı⁄U•¢Ã◊¥~Á∑§◊Ë¬Ífl¸∑§Ë•Ù⁄Uø‹ÃË„ÒU— (i) ø‹ËªÿËŒÍ⁄UËÄÿÊ„ÒU? (ii)¬Á⁄UáÊÊ◊ËÁflSÕÊ¬ŸÄÿÊ„ÒU? vÆ. ∞∑§øË¥≈UËP‚QÃ∑§}‚◊ËŒÍ⁄UËø‹ÃË„ÒU•ı⁄UÁ»§⁄UPQ‚‚◊∑§ÙáÊ¬⁄U{‚◊ËŒÍ⁄UËø‹ÃË„ÒU–ß‚∑§Ê¬Á⁄UáÊÊ◊ËÁflSÕÊ¬ŸôÊÊÃ∑§ËÁ¡∞– ©UûÊ⁄U — w.πR;wR {.(•){Á∑§◊Ë(’)‡ÊÍãÿ~.(i)v{Á∑§◊Ë(ii)vw.{Á∑§◊ËvÆ.vÆ‚◊Ë–

∞∑§ ‚◊ÊŸ ∞fl¢ •‚◊ÊŸ ªÁÃ (UniFoRM AnD non-UniFoRM Motion)

Á∑§‚Ë flSÃÈ ◊¥ ∞∑§ ‚◊ÊŸ ªÁÃ „UÙÃË „ÒU, ÿÁŒ fl„U ‚◊ÿ ∑§ ’⁄UÊ’⁄U •¢Ã⁄UÊ‹Ù¥ ◊¥ ’⁄UÊ’⁄U ŒÍÁ⁄UÿÊ° ø‹ÃË „ÒU, ÿ„U ‚◊ÿ •¢Ã⁄UÊ‹ øÊ„U Á∑§ÃŸ ¿UÙ≈U ÄÿÙ¥ Ÿ „UÙ¥– ©UŒÊ„U⁄UáÊÊÕ¸,◊ÊŸ‹¥vÆ◊Ë≈U⁄U¬˝ÁÃ‚∑§á«U∑§ËÁSÕ⁄UøÊ‹‚ø‹ÃË„ÈUß¸∞∑§∑§Ê⁄U,vÆ◊Ë≈U⁄U∑§Ë’⁄UÊ’⁄UŒÍÁ⁄UÿÊ°Ãÿ∑§⁄UªË,ß‚Á‹∞©U‚∑§ËªÁÃ∞∑§‚◊ÊŸ„UÙªË–∑Î§¬ÿÊŸÙ≈U∑§⁄¥UÁ∑§∞∑§ ‚◊ÊŸ ªÁÃ ∑§ Á‹∞ ŒÍ⁄UË-‚◊ÿ ª˝Ê»§ ∞∑§ ‚ËœË ⁄UπÊ „UÙÃÊ „ÒU (¡Ò‚ÊÁ∑§ÁøòÊz◊¥ÁŒπÊÿÊªÿÊ„ÒU)–

Á∑§‚Ë flSÃÈ ◊¥ •‚◊ÊŸ ªÁÃ „UÙÃË „ÒU, ÿÁŒ fl„U ‚◊ÿ ∑§ ’⁄UÊ’⁄U •¢Ã⁄UÊ‹Ù¥ ◊¥ •‚◊ÊŸ ŒÍÁ⁄UÿÊ° ø‹ÃË „ÒU– ©UŒÊ„U⁄UáÊÊÕ¸,ÿÁŒ„U◊∞∑§ª¥Œ∑§Ù™°§øËß◊Ê⁄UÃ∑§Ë¿UÃ‚Áª⁄UÊÃ„Ò¥U,„U◊¬Êÿ¥ªÁ∑§fl„U‚◊ÿ∑§’⁄UÊ’⁄U•ãÃ⁄UÊ‹Ù¥◊¥•‚◊ÊŸŒÍÁ⁄UÿÊ°Ãÿ∑§⁄UÃÊ„ÒU–fl„UÃÿ∑§⁄UÃÊ„ÒU—

¬„U‹‚∑§á«U◊¥y.~◊Ë≈U⁄UŒÍ‚⁄U‚∑§á«U◊¥vy.|◊Ë≈U⁄UÃË‚⁄U‚∑§á«U◊¥wy.z◊Ë≈U⁄U,ßàÿÊÁŒ,ßàÿÊÁŒ–ß‚¬˝∑§Ê⁄U,SflÃãòÊM§¬‚Áª⁄UÃÊ„ÈU•Êª¥Œ,¬˝Ê⁄UÁê÷∑§“v‚∑§á«U”∑§•¢Ã⁄UÊ‹Ù¥◊¥¿UÙ≈UË(ÿÊ∑§◊)

ŒÍÁ⁄UÿÊ°Ãÿ∑§⁄UÃÊ„ÒU•ı⁄U’ÊŒ◊¥“v‚∑§á«U”∑§•¢Ã⁄UÊ‹Ù¥◊¥’«∏UË(ÿÊ•Áœ∑§)ŒÍÁ⁄UÿÊ°Ãÿ∑§⁄UÃÊ„ÒU–ß‚‚„U◊ÁŸc∑§·¸ÁŸ∑§Ê‹Ã„Ò¥UÁ∑§SflÃãòÊ M§¬ ‚ Áª⁄UÃË „ÈUß¸ flSÃÈ ∑§Ë ªÁÃ, •‚◊ÊŸ ªÁÃ ∑§Ê ©UŒÊ„U⁄UáÊ „ÒU– ⁄U‹flS≈U‡ÊŸ‚⁄U‹ªÊ«∏UË¿ÍU≈UŸ∑§ËªÁÃ÷Ë•‚◊ÊŸªÁÃ∑§Ê©UŒÊ„U⁄UáÊ„ÒU–∑§Ê⁄UáÊÿ„U„ÒUÄÿÙ¥Á∑§¡’⁄U‹ªÊ«∏UËS≈U‡ÊŸ‚¿ÍU≈UÃË„ÒU,fl„U“¬„U‹‚∑§á«U”◊¥’„ÈUÃ∑§◊ŒÍ⁄UËÃÿ∑§⁄UÃË„ÒU–“ŒÍ‚⁄U”‚∑§á«U◊¥⁄U‹ªÊ«∏UË∑È§¿U•Áœ∑§ŒÍ⁄UËÃÿ∑§⁄UÃË„ÒU•ı⁄Uß‚Ë¬˝∑§Ê⁄UŒÍ⁄UË’…∏UÃË¡ÊÃË„ÒU–•ı⁄U¡’⁄U‹ªÊ«∏UË•ª‹S≈U‡ÊŸ¬⁄U¬„È°UøŸflÊ‹Ë„UÙÃË„ÒU,©U‚∑§mÊ⁄UÊÃÿ∑§ËªÿËŒÍ⁄UË¬ÁÃ‚∑§á«U∑§◊„UÙÃË¡ÊÃË„ÒU–∑Î§¬ÿÊŸÙ≈U∑§⁄¥UÁ∑§•‚◊ÊŸ ªÁÃ flÊ‹Ë flSÃÈ ∑§Ê ŒÍ⁄UË-‚◊ÿ ª˝Ê»§fl∑˝§ ⁄UπÊ „UÙÃÊ „ÒU (¡Ò‚ÊÁ∑§ÁøòÊ{◊¥ÁŒπÊÿÊªÿÊ„ÒU)–•Ã—,ôÊÊÃ∑§⁄UŸ∑§Á‹∞Á∑§flSÃÈ∑§ËªÁÃ∞∑§‚◊ÊŸ„ÒU•ÕflÊ•‚◊ÊŸ„ÒU,„U◊¥©U‚∑§Á‹∞ŒÍ⁄UË-‚◊ÿª˝Ê»§πË¥øŸÊ„UÙªÊ–ÿÁŒŒÍ⁄UË-‚◊ÿª˝Ê»§∞∑§‚ËœË-⁄UπÊ„ÒU,ªÁÃ∞∑§‚◊ÊŸ„UÙªË•ı⁄UÿÁŒŒÍ⁄UË-‚◊ÿª˝Ê»§∞∑§fl∑˝§⁄UπÊ„ÒU,ªÁÃ•‚◊ÊŸ„UÙªË–ÿ„UŸÙ≈U∑§⁄UŸÊ„UÙªÊÁ∑§•‚◊ÊŸ ªÁÃ, àflÁ⁄UÃ ªÁÃ ÷Ë ∑§„U‹ÊÃË „ÒU–

ÁøòÊ z. ∞∑§‚◊ÊŸªÁÃflÊ‹ËflSÃÈ∑§ Á‹∞ŒÍ⁄UË-‚◊ÿª˝Ê»§‚ËœË⁄UπÊ„UÙÃÊ„ÒU–

ÁøòÊ {. •‚◊ÊŸªÁÃflÊ‹ËflSÃÈ∑§Á‹∞ŒÍ⁄UË-‚◊ÿª˝Ê»§fl∑˝§⁄UπÊ„UÙÃÊ„ÒU–


øÊ‹, flª •ı⁄U àfl⁄UáÊ (Speed, Velocity and Acceleration) Á∑§‚ËflSÃÈ∑§ËªÁÃ∑§ÊfláÊ¸ŸÃËŸ‡ÊéŒÙ¥mÊ⁄UÊÁ∑§ÿÊ¡Ê‚∑§ÃÊ„ÒU—øÊ‹(speed),flª(velocity)•ı⁄Uàfl⁄UáÊ(acceleration)–∞∑§-∞∑§

∑§⁄U∑§,„U◊©UŸ∑§ÊÁflSÃÊ⁄U‚•äÿÿŸ∑§⁄UÃ„Ò¥U–

øÊ‹ (SPEED)

∑§Ùß¸∑§Ê⁄UÿÁŒœË⁄U-œË⁄Uø‹⁄U„UË„ÒU,„U◊∑§„UÃ„Ò¥UÁ∑§©U‚∑§ËøÊ‹∑§◊„ÒU–•ı⁄UÿÁŒ∑§Ê⁄UÃ¡ø‹⁄U„UË„UÙÃË„ÒU,ÃÙ„U◊∑§„UÃ„Ò¥UÁ∑§©U‚∑§ËøÊ‹•Áœ∑§„ÒU–•Ã—,Á∑§‚Ë flSÃÈ ∑§Ë øÊ‹ ÿ„U ÁfløÊ⁄U ŒÃË „ÒU Á∑§ fl„U flSÃÈ Á∑§ÃŸË ◊¢Œ •ÕflÊ Ã¡ ø‹ ⁄U„UË „ÒU– „U◊•’Á∑§‚ËªÁÃ‡ÊË‹flSÃÈ∑§ËøÊ‹∑§ÙÁŸêŸ¬˝∑§Ê⁄U¬Á⁄U÷ÊÁ·Ã∑§⁄U‚∑§Ã„Ò¥U—Á∑§‚Ë flSÃÈ ∑§Ë øÊ‹, ©U‚∑§ mÊ⁄UÊ ¬˝ÁÃ ß∑§Êß¸ ‚◊ÿ ◊¥ ø‹Ë ªÿË ŒÍ⁄UË „ÒU– flSÃÈ∑§ËøÊ‹∑§Ù,ß‚ŒÍ⁄UË∑§ÙÃÿ∑§⁄UŸ◊¥Á‹ÿ ªÿ ‚◊ÿ mÊ⁄UÊ ø‹Ë ªÿË ŒÍ⁄UË ∑§Ù÷ÊªŒ∑§⁄U¬Á⁄U∑§Á‹ÃÁ∑§ÿÊ¡Ê‚∑§ÃÊ„ÒU–ß‚Á‹∞,øÊ‹∑§Á‹∞‚ÍòÊ∑§ÙÁŸêŸ¬˝∑§Ê⁄UÁ‹πÊ¡Ê‚∑§ÃÊ„ÒU—

øÊ‹ =

ÿÁŒ∑§Ùß¸flSÃÈt‚◊ÿ◊¥,ŒÍ⁄UËsø‹ÃË„ÒU,ÃÙ©U‚∑§ËøÊ‹v∑§ÙÁŸêŸ¬˝∑§Ê⁄UÁŒÿÊ¡Ê‚∑§ÃÊ„ÒU—

v =st

¡„UÊ°, v = øÊ‹ s = ø‹ËªÿËŒÍ⁄UË •ı⁄Ut = Á‹ÿÊªÿÊ‚◊ÿ(©U‚ŒÍ⁄UË∑§ø‹Ÿ◊¥)◊ÊŸ‹¥∞∑§∑§Ê⁄UyÉÊá≈U◊¥vÆÆÁ∑§‹Ù◊Ë≈U⁄U∑§ËŒÍ⁄UËÃÿ∑§⁄UÃË„ÒU,ÃÙß‚∑§Ê⁄U∑§ËøÊ‹∑§Ùß‚¬˝∑§Ê⁄UÁŒÿÊ¡Ê‚∑§ÃÊ„ÒU—

øÊ‹ =

•ÕflÊ øÊ‹ = wzÁ∑§‹Ù◊Ë≈U⁄U¬˝ÁÃÉÊá≈UÊ(ÿÊwzkm/h)•Ã—,ß‚∑§Ê⁄U∑§ËøÊ‹wzÁ∑§‹Ù◊Ë≈U⁄U¬˝ÁÃÉÊá≈UÊ„UÙªË–ß‚∑§Ê•Õ¸„ÒUÁ∑§∑§Ê⁄U“¬˝àÿ∑§ÉÊá≈U”◊¥wzÁ∑§‹Ù◊Ë≈U⁄U∑§ËŒÍ⁄UËÃÿ∑§⁄UÃË„ÒU–øÊ‹

∑§ËªáÊŸÊ∑§⁄UŸ∑§Á‹∞©U¬ÿÈ¸Q§ÁŒÿªÿ‚ÍòÊ◊¥ÃËŸ⁄UÊÁ‡ÊÿÊ°„UÙÃË„Ò¥U—øÊ‹,ø‹ËªÿËŒÍ⁄UËÃÕÊÁ‹ÿÊªÿÊ‚◊ÿ–„U◊¥ÿÁŒÁ∑§ã„UË¥ŒÙ⁄UÊÁ‡ÊÿÙ¥∑§Ê◊ÍÀÿÁŒÿÊ„UÙÃÊ„ÒU,ÃÙß‚‚ÍòÊ∑§Ê©U¬ÿÙª∑§⁄U∑§ÃË‚⁄UË⁄UÊÁ‡Ê∑§◊ÍÀÿ∑§ËªáÊŸÊ∑§Ë¡Ê‚∑§ÃË„ÒU–

ŒÍ⁄UË∑§Ê∞‚.•Êß¸.◊ÊòÊ∑§(SI Unit)◊Ë≈U⁄U(m)„ÒU•ı⁄U‚◊ÿ∑§Ê‚∑§á«U(s)„ÒU,ß‚Á‹∞,øÊ‹ ∑§Ê ∞‚.•Êß¸. ◊ÊòÊ∑§ (Si Unit) ◊Ë≈U⁄U ¬˝ÁÃ ‚∑§á«U „UÙÃÊ „ÒU Á¡‚m/sÿÊms–1∑§M§¬◊¥Á‹πÊ¡ÊÃÊ„ÒU–øÊ‹∑§¿UÙ≈U◊ÍÀÿÙ¥∑§Ù‚ã≈UË◊Ë≈U⁄U ¬˝ÁÃ ‚∑§á«U ∑§◊ÊòÊ∑§Ù¥◊¥√ÿQ§Á∑§ÿÊ¡ÊÃÊ„ÒUÁ¡‚cm/sÿÊcm s–1∑§M§¬◊¥Á‹πÊ¡ÊÃÊ„ÒU–•Áœ∑§øÊ‹∑§◊ÍÀÿÙ¥∑§Ù√ÿQ§∑§⁄UŸ∑§Á‹∞,„U◊Á∑§‹Ù◊Ë≈U⁄U ¬˝ÁÃ ÉÊá≈U ∑§Ê◊ÊòÊ∑§©U¬ÿÙª∑§⁄UÃ„Ò¥UÁ¡‚km.p.h.ÿÊkm/hÿÊkm h–1∑§M§¬◊¥Á‹πÊ¡ÊÃÊ„ÒU–∑Î§¬ÿÊŸÙ≈U∑§⁄¥UÁ∑§ÿÁŒ„U◊¥∑§ß¸flSÃÈ•Ù¥∑§øÊ‹Ù¥∑§ËÃÈ‹ŸÊ∑§⁄UŸË„ÒU,ÃÙ„U◊¥©U‚Ë◊ÊòÊ∑§◊¥©UŸ‚÷Ë∑§ËøÊ‹Ù¥∑§Ù√ÿQ§∑§⁄UŸÊøÊÁ„U∞–øÊ‹◊¥∑§fl‹¬Á⁄U◊ÊáÊ(magnitude)„UÙÃÊ„ÒU,©U‚◊¥∑§Ùß¸ÁflÁ‡ÊCÔUÁŒ‡ÊÊŸ„UË¥„UÙÃË„ÒU,ß‚Á‹∞,øÊ‹ ∞∑§ •ÁŒ‡Ê ⁄UÊÁ‡Ê (scalar quantity) „ÒU–

‚◊ÿ∑§Á∑§‚Ë÷ËˇÊáÊ,ø‹ÃË„ÈUß¸∑§Ê⁄U∑§ËøÊ‹∑§ÙøÊ‹◊Ê¬Ë (speedometer)ŸÊ◊∑§©U¬∑§⁄UáÊmÊ⁄UÊŒπÊ¡Ê‚∑§ÃÊ„ÒU¡Ù∑§Ê⁄U◊¥‹ªÊ„UÙÃÊ„ÒU–øÊ‹◊Ê¬Ë,øÊ‹∑§ÙÁ∑§‹Ù◊Ë≈U⁄U¬˝ÁÃÉÊá≈U◊¥’Ã‹ÊÃÊ„ÒU–∑§Ê⁄UmÊ⁄UÊø‹ËªÿËŒÍ⁄UË∑§Ù¬Õ◊Ê¬Ë (odometer)ŸÊ◊∑§∞∑§•ãÿ©U¬∑§⁄UáÊmÊ⁄UÊ÷Ë◊Ê¬Ê¡ÊÃÊ„ÒUÁ¡‚÷Ë∑§Ê⁄U◊¥‚¢SÕÊÁ¬ÃÁ∑§ÿÊ¡ÊÃÊ„ÒU–ÿ„UŒÍ⁄UË∑§ÙÁ∑§‹Ù◊Ë≈U⁄UÙ¥◊¥Á⁄U∑§Ê«¸U∑§⁄UÃÊ„ÒU–

•ı‚Ã øÊ‹ (Average Speed) ø‹Ë ªÿË ∑È§‹ ŒÍ⁄UË ∑§Ù, ß‚ ŒÍ⁄UË ∑§Ù Ãÿ ∑§⁄UŸ ◊¥ ‹ª „ÈU∞ ∑È§‹ ‚◊ÿ mÊ⁄UÊ ÷Êª ŒŸ ‚ ¬˝Ê# ÷Êª»§‹ flSÃÈ ∑§Ë •ı‚Ã ŒÍ⁄UË „UÙÃË „ÒU–

∑§Ê⁄U(ÿÊ’‚)◊¥ÿÊòÊÊ∑§⁄UÃ‚◊ÿ„U◊ŸäÿÊŸÁŒÿÊ„ÒUÁ∑§∑§Ê⁄U∑§ËøÊ‹∑§ÙÁSÕ⁄UÿÊ∞∑§‚◊ÊŸ⁄Uπ¬ÊŸÊ’„ÈUÃ∑§Á∆UŸ„UÙÃÊ„ÒUÄÿÙ¥Á∑§∑§ß¸SÕÊŸÙ¥¬⁄UÁflÁ÷ãŸ∑§Ê⁄UáÊÙ¥‚∑§Ê⁄U∑§Ù⁄UÙ∑§ŸÿÊœË◊Ë∑§⁄UŸ∑§Á‹∞’˝∑§Ù¥∑§Ù‹ªÊŸÊ¬«∏UÃÊ„ÒU–•Ã—,flSÃÈ∑§ËøÊ‹¬˝Êÿ—ÁSÕ⁄UŸ„UË¥„UÙÃË„ÒU•ı⁄Uø‹ËªÿËŒÍ⁄UË∑§Ù‚◊ÿmÊ⁄UÊ÷ÊªŒŸ‚„U◊¥©U‚‚◊ÿ∑§Œı⁄UÊŸ•ı‚ÃøÊ‹¬˝Ê#„UÙÃË„ÒU–©UŒÊ„U⁄UáÊÊÕ¸,∞∑§∑§Ê⁄U∑§Á‹∞¡ÙyÉÊá≈U◊¥vÆÆÁ∑§◊Ë

∑§ËŒÍ⁄UËÃÿ∑§⁄UÃË„ÒU,•ı‚ÃøÊ‹100 25

4= Á∑§◊Ë¬˝ÁÃÉÊá≈UÊ„UÙÃË„ÒU–ÿlÁ¬ß‚∑§Ê⁄U∑§Ë•ı‚ÃøÊ‹wzÁ∑§◊Ë¬˝ÁÃÉÊá≈UÊ„ÒU,ß‚∑§Ê•Õ¸

ÿ„UŸ„UË¥„ÒUÁ∑§∑§Ê⁄U¬Í⁄U‚◊ÿß‚ËøÊ‹‚ªÁÃ◊ÊŸ⁄U„UÃË„ÒU–¡’‚«∏U∑§‚ËœË,øı⁄U‚•ı⁄UπÊ‹Ë„UÙÃË„ÒU,øÊ‹wzÁ∑§◊Ë¬˝ÁÃÉÊá≈UÊ‚∑§Ê»§Ë

xfr 9

•Áœ∑§„UÙ‚∑§ÃË„ÒU,¬⁄UãÃÈ◊Ù«∏UÙ¥(fl∑˝§Ë‚«∏U∑§),¬„UÊ«∏UÙ¥¬⁄U•ÕflÊ÷Ë«∏U-÷Ê«∏UflÊ‹ˇÊòÊ◊¥øÊ‹ß‚•ı‚Ã◊ÍÀÿ‚∑§Ê»§ËŸËøÁª⁄U‚∑§ÃË„ÒU–„U◊¥ÿÊŒ⁄UπŸÊ„UÙªÊÁ∑§—

•ı‚ÃøÊ‹ =

ÕÙ«∏UË„UËŒ⁄U◊¥,•Ê¢Á∑§∑§‚◊SÿÊ•Ù¥∑§Ù„U‹∑§⁄UŸ∑§Á‹∞,„U◊ß‚‚ÍòÊ∑§Ê©U¬ÿÙª∑§⁄¥Uª–

∞∑§ ‚◊ÊŸ øÊ‹ (ÿÊ ÁSÕ⁄U øÊ‹) [Uniform Speed (or Constant Speed)] flSÃÈ ◊¥ ∞∑§ ‚◊ÊŸ øÊ‹ „UÙÃË „ÒU, ÿÁŒ fl„U ‚◊ÿ ∑§ ‚◊ÊŸ •¢Ã⁄UÊ‹Ù¥ ◊¥ ‚◊ÊŸ ŒÍ⁄UË Ãÿ ∑§⁄UÃË „ÒU, fl ‚◊ÿ •¢Ã⁄UÊ‹ Á∑§ÃŸ „UË ¿UÙ≈U ÄÿÙ¥

Ÿ „UÙ¥– ©UŒÊ„U⁄UáÊÊÕ¸,∞∑§∑§Ê⁄U∑§ËøÊ‹∞∑§‚◊ÊŸªÁÃflÊ‹Ë,◊ÊŸÊ{ÆÁ∑§◊Ë¬˝ÁÃÉÊá≈UÊ,∑§„UË¡ÊÃË„ÒU,ÿÁŒfl„U¬˝àÿ∑§•ÊœÉÊá≈U◊¥xÆÁ∑§◊Ë,

¬˝àÿ∑§øıÕÊß¸ÉÊá≈U◊¥vzÁ∑§◊Ë,¬˝àÿ∑§Á◊Ÿ≈U◊¥vÁ∑§◊Ë,•ı⁄U¬˝àÿ∑§‚∑§á«U◊¥160

Á∑§◊Ëø‹ÃË„ÒU–¡Ò‚ÊÁ∑§„U◊™§¬⁄U¬„U‹„UËøøÊ¸∑§⁄U

øÈ∑§„Ò¥UÁ∑§flSÃÈÃ—√ÿfl„UÊ⁄UM§¬◊¥flSÃÈ∑§ËøÊ‹∞∑§‹ê’‚◊ÿÃ∑§∑§Á∆UŸÊß‚„UË∞∑§‚◊ÊŸ(•ÕflÊÁSÕ⁄U)⁄U„U¬ÊÃË„ÒU–Á»§⁄U÷ËflSÃÈ∑§ËøÊ‹∑§ÙÿÁŒÁSÕ⁄U‚◊¤ÊÁ‹ÿÊ¡Êÿ,ÃÙ„U◊∆UË∑§-∆UË∑§ôÊÊÃ∑§⁄U‚∑§Ã„Ò¥UÁ∑§ÁŒÿ„ÈU∞‚◊ÿ◊¥Á∑§ÃŸËŒÍ⁄UËÃÿ∑§⁄UªË•ÕflÊÿÁŒ„U◊flSÃÈmÊ⁄UÊø‹ËªÿËŒÍ⁄UË∑§Ù¡ÊŸÃ„Ò¥U,©U‚ŒÍ⁄UË∑§ø‹Ÿ◊¥‹ªÊÿªÿ‚◊ÿ∑§Ë„U◊ªáÊŸÊ∑§⁄U‚∑§Ã„Ò¥U–•’„U◊øÊ‹¬⁄U•ÊœÊÁ⁄UÃ∑È§¿U‚◊SÿÊ∞°„U‹∑§⁄¥Uª–

Ÿ◊ÍŸÊÕ¸ ‚◊SÿÊ v. ∞∑§S∑Í§≈U⁄UøÊ‹∑§zÁ◊Ÿ≈U◊¥xÁ∑§‹Ù◊Ë≈U⁄U∑§ËŒÍ⁄UËÃÿ∑§⁄UÃÊ„ÒU–ÁŸêŸÁ‹ÁπÃ◊¥øÊ‹∑§ËªáÊŸÊ∑§ËÁ¡∞—(•)‚¥≈UË◊Ë≈U⁄U¬˝ÁÃ‚∑§á«U(cm/s) (’)◊Ë≈U⁄U¬˝ÁÃ‚∑§á«U(m/s) (‚)Á∑§‹Ù◊Ë≈U⁄U¬˝ÁÃÉÊá≈UÊ(km/h)„U‹ — (•)‚¥≈UË◊Ë≈U⁄U¬˝ÁÃ‚∑§á«U◊¥øÊ‹∑§ËªáÊŸÊ∑§⁄UŸ∑§Á‹∞,ŒË„ÈUß¸xÁ∑§‹Ù◊Ë≈U⁄U∑§ËŒÍ⁄UË∑§Ù„U◊¥‚¥≈UË◊Ë≈U⁄U◊¥•ı⁄UÁŒÿ„ÈUÿ‚◊ÿ

zÁ◊Ÿ≈U∑§Ù‚∑§á«U◊¥’Œ‹ŸÊ„UÙªÊ–∑Î§¬ÿÊŸÙ≈U∑§⁄¥UÁ∑§vÁ∑§‹Ù◊Ë≈U⁄U◊¥vÆÆÆ◊Ë≈U⁄U•ı⁄Uv◊Ë≈U⁄U◊¥vÆÆ‚¥≈UË◊Ë≈U⁄U„UÙÃ„Ò¥U–•’, ø‹ËªÿËŒÍ⁄UË = xkm = x×vÆÆÆm = x×vÆÆÆ×vÆÆcm = xÆÆ,ÆÆÆcm ...(v) Á‹ÿÊªÿÊ‚◊ÿ = zÁ◊Ÿ≈U = z×{Æ‚∑§á«U = xÆÆs ...(w)

„U◊¡ÊŸÃ„Ò¥UÁ∑§, øÊ‹ =

=300,000 cm

300 s = vÆÆÆcm/s ...(x)•Ã—,S∑Í§≈U⁄UøÊ‹∑§∑§ËøÊ‹vÆÆÆ‚¥≈UË◊Ë≈U⁄U¬˝ÁÃ‚∑§á«U„ÒU–(’)øÊ‹∑§Ù◊Ë≈U⁄U¬˝ÁÃ‚∑§á«U◊¥√ÿQ§∑§⁄UŸ∑§Á‹∞,„U◊¥ŒËªÿËŒÍ⁄UËxÁ∑§‹Ù◊Ë≈U⁄U∑§Ù◊Ë≈U⁄U◊¥•ı⁄UÁŒÿ„ÈU∞‚◊ÿzÁ◊Ÿ≈U∑§Ù‚∑§á«U

◊¥’Œ‹ŸÊ„UÙªÊ–•Ã—,ß‚∑§‚◊¥— ø‹ËªÿËŒÍ⁄UË = xkm = x×vÆÆÆm = xÆÆÆm ...(y) Á‹ÿÊªÿÊ‚◊ÿ = zÁ◊Ÿ≈U = z×{Æ‚∑§á«U = xÆÆs ...(z)

•’, øÊ‹ =

=3000 m300 s

= vÆm/s ...({)


ß‚Á‹∞,S∑Í§≈U⁄UøÊ‹∑§∑§ËøÊ‹vÆ◊Ë≈U⁄U¬˝ÁÃ‚∑§á«U„ÒU–(‚)•ı⁄U•¢Ã◊¥,Á∑§‹Ù◊Ë≈U⁄U¬˝ÁÃÉÊá≈UÊ◊¥øÊ‹∑§ËªáÊŸÊ∑§⁄UŸ∑§Á‹∞ŒË„ÈUß¸ŒÍ⁄UË∑§ÙÁ∑§‹Ù◊Ë≈U⁄U◊¥(¡Ù¬„U‹‚„UË„ÒU)•ı⁄UÁŒÿ„ÈU∞

‚◊ÿ∑§ÙÉÊá≈UÙ¥◊¥√ÿQ§∑§⁄UŸÊ„UÙªÊ–ß‚Á‹∞,ß‚∑§‚◊¥— ø‹ËªÿËŒÍ⁄UË = xkm ...(|) Á‹ÿÊªÿÊ‚◊ÿ = zÁ◊Ÿ≈U

=560

ÉÊá≈U

= Æ.Æ}xh ...(})


=3 km

0.083 h = x{km/h ...(~)•Ã—,S∑Í§≈U⁄UøÊ‹∑§∑§ËøÊ‹x{Á∑§‹Ù◊Ë≈U⁄U¬˝ÁÃÉÊá≈UÊ„ÒU–Ÿ◊ÍŸÊÕ¸ ‚◊SÿÊ w. ∞∑§⁄U‹ªÊ«∏UËA,xÉÊá≈U◊¥vwÆÁ∑§◊Ë∑§ËŒÍ⁄UËÃÿ∑§⁄UÃË„ÒU¡’Á∑§∞∑§•ãÿ⁄U‹ªÊ«∏UËB,yÉÊá≈U◊¥v}ÆÁ∑§◊Ë∑§ËŒÍ⁄UË

Ãÿ∑§⁄UÃË„ÒU–∑§ıŸ-‚Ë⁄U‹ªÊ«∏UËÃ¡ø‹ÃË„ÒU?„U‹ — ß‚‚◊SÿÊ∑§Ù„U‹∑§⁄UŸ∑§Á‹∞„U◊¥•‹ª-•‹ªŒÙŸÙ¥⁄U‹ªÊÁ«∏UÿÙ¥∑§ËøÊ‹Ù¥∑§ËªáÊŸÊ∑§⁄UŸË„UÙÃË„ÒU–©UìÊÃ⁄UøÊ‹flÊ‹Ë⁄U‹ªÊ«∏UË

Ã¡ø‹ÃË„ÒU–(i)„U◊¡ÊŸÃ„Ò¥UÁ∑§,

øÊ‹ =

•’,⁄U‹ªÊ«∏UËAmÊ⁄UÊø‹ËªÿËŒÍ⁄UË=vwÆkm•ı⁄U,⁄U‹ªÊ«∏UËAmÊ⁄UÊÁ‹ÿÊªÿÊ‚◊ÿ=xh

ß‚Á‹∞,⁄U‹ªÊ«∏UËA∑§ËøÊ‹=120 km

3 h=yÆkm/h ...(v)•Ã—,⁄U‹ªÊ«∏UËA∑§ËøÊ‹yÆÁ∑§‹Ù◊Ë≈U⁄U¬˝ÁÃÉÊá≈UÊ„ÒU–

(ii)¬ÈŸ—, øÊ‹ =

•’, ⁄U‹ªÊ«∏UËBmÊ⁄UÊø‹ËªÿËŒÍ⁄UË = v}Ækm•ı⁄U ⁄U‹ªÊ«∏UËBmÊ⁄UÊÁ‹ÿÊªÿÊ‚◊ÿ = yh

ß‚Á‹∞, ⁄U‹ªÊ«∏UËB∑§ËøÊ‹ =180 km

4 h = yzkm/h ...(w)

•Ã—,⁄U‹ªÊ«∏UËB∑§ËøÊ‹yzÁ∑§‹Ù◊Ë≈U⁄U¬˝ÁÃÉÊá≈UÊ„ÒU–©U¬ÿÈ¸Q§ªáÊŸÊ•Ù¥‚„U◊¬ÊÃ„Ò¥UÁ∑§⁄U‹ªÊ«∏UËA∞∑§ÉÊá≈U◊¥yÆÁ∑§‹Ù◊Ë≈U⁄U∑§ËŒÍ⁄UËÃÿ∑§⁄UÃË„ÒU¡’Á∑§⁄U‹ªÊ«∏UËB∞∑§ÉÊá≈U◊¥yzÁ∑§‹Ù◊Ë≈U⁄U

∑§ËŒÍ⁄UËÃÿ∑§⁄UÃË„ÒU–ÄÿÙ¥Á∑§⁄U‹ªÊ«∏UËB∑§ËøÊ‹©UìÊÃ⁄U„ÒU,ß‚Á‹∞,⁄U‹ªÊ«∏UËBÃ¡ø‹ÃË„ÒU–Ÿ◊ÍŸÊÕ¸ ‚◊SÿÊ x. ∞∑§∑§Ê⁄UyÆkm/h∑§Ë∞∑§‚◊ÊŸøÊ‹‚xÆkmø‹ÃË„ÒU•ı⁄U•ª‹ËxÆkm,wÆkm/h∑§Ë∞∑§‚◊ÊŸøÊ‹‚

ø‹ÃË„ÒU–©U‚∑§Ë•ı‚ÃøÊ‹ôÊÊÃ∑§ËÁ¡∞–„U‹ — (i)∑§Ê⁄U¬„U‹yÆÁ∑§‹Ù◊Ë≈U⁄U¬˝ÁÃÉÊá≈U∑§ËøÊ‹‚xÆÁ∑§‹Ù◊Ë≈U⁄U∑§ËŒÍ⁄UËÃÿ∑§⁄UÃË„ÒU–„U◊,∑§Ê⁄UmÊ⁄UÊÿ„UŒÍ⁄UËÃÿ∑§⁄UŸ◊¥Á‹ÿÊ

ªÿÊ‚◊ÿôÊÊÃ∑§⁄UÃ„Ò¥U–ÿ„UÊ°, øÊ‹ = yÆkm/h

xfr 11

ŒÍ⁄UË = xÆkm •ı⁄U, ‚◊ÿ = ?(ªáÊŸÊ∑§⁄UŸÊ„ÒU)


ß‚Á‹∞, yÆ =

•ı⁄U, ‚◊ÿ =3040

ÉÊá≈U

•ÕflÊ, ‚◊ÿ(t1) =34

ÉÊá≈U ...(v)

(ii)ß‚∑§’ÊŒ∑§Ê⁄UwÆkm/h∑§ËøÊ‹‚xÆkm∑§ËŒÍ⁄UËÃÿ∑§⁄UÃË„ÒU–„U◊,ß‚ŒÍ⁄UË∑§ÙÃÿ∑§⁄UŸ◊¥∑§Ê⁄UmÊ⁄UÊÁ‹ÿªÿ‚◊ÿ∑§Ù÷ËôÊÊÃ∑§⁄UÃ„Ò¥U–ß‚∑§‚◊¥—

øÊ‹ = wÆkm/h ŒÍ⁄UË = xÆkm•ı⁄U, ‚◊ÿ = ?(ªáÊŸÊ∑§⁄UŸÊ„ÒU)

¬ÈŸ—, øÊ‹ =

ß‚Á‹∞, wÆ =

•ı⁄U, ‚◊ÿ =3020

ÉÊá≈U

•ÕflÊ, ‚◊ÿ(t2) =32

ÉÊá≈U ...(w)

©U¬ÿÈ¸Q§ŒÙ‚◊ÿ◊ÍÀÿÙ¥t1•ı⁄Ut2∑§Ù¡Ù«∏U∑§⁄U,„U◊¬Í⁄UËÿÊòÊÊ◊¥∑§Ê⁄UmÊ⁄UÊÁ‹ÿÊªÿÊ‚◊ÿôÊÊÃ∑§⁄U‚∑§Ã„Ò¥U–•Ã—,

Á‹ÿÊªÿÊ∑È§‹‚◊ÿ =3 34 2+ ÉÊá≈U

=3 6

4+

ÉÊá≈U

=94

ÉÊá≈U ...(x)

•ı⁄U, ø‹ËªÿË∑È§‹ŒÍ⁄UË = xÆkm +xÆkm = {Ækm ...(y)

•’, •ı‚ÃøÊ‹ =

=60 4

9×

=2409

= w{.{km/h•Ã—,‚ê¬ÍáÊ¸ÿÊòÊÊ◊¥∑§Ê⁄U∑§Ë•ı‚ÃøÊ‹w{.{Á∑§‹Ù◊Ë≈U⁄U¬˝ÁÃÉÊá≈UÊ„ÒU–Ÿ◊ÍŸÊÕ¸ ‚◊SÿÊ y. vwÆkm◊Êª¸¬⁄U,⁄U‹ªÊ«∏UË¬„U‹xÆkm/h∑§Ë∞∑§‚◊ÊŸøÊ‹‚xÆkmø‹ÃË„ÒU–•ª‹~ÆkmÃÿ∑§⁄UŸ∑§

Á‹∞⁄U‹ªÊ«∏UËÁ∑§ÃŸËÃ¡ø‹Á∑§¬Í⁄UËÿÊòÊÊ◊¥•ı‚ÃøÊ‹{Ækm/h„UÙ¡Êÿ?„U‹ — ß‚•Ê¢Á∑§∑§‚◊SÿÊ◊¥„U◊¥,⁄U‹ªÊ«∏UËmÊ⁄UÊø‹ËªÿË∑È§‹ŒÍ⁄UË(¡ÙvwÆkm„ÒU),•ı⁄U‚ê¬ÍáÊ¸ÿÊòÊÊ∑§Á‹∞⁄U‹ªÊ«∏UË∑§Ë•ı‚ÃøÊ‹

(¡Ù{Ækm/h„ÒU)ŒË„ÈUß¸„ÒU–ßŸŒÙŸÙ¥◊ÍÀÿÙ¥‚,„U◊¬Í⁄UËÿÊòÊÊ◊¥⁄U‹ªÊ«∏UËmÊ⁄UÊÁ‹ÿªÿ‚◊ÿ∑§ËªáÊŸÊ∑§⁄U‚∑§Ã„Ò¥U–ß‚ÁŸêŸ¬˝∑§Ê⁄UÁ∑§ÿÊ¡Ê‚∑§ÃÊ„ÒU—


„U◊¡ÊŸÃ„Ò¥UÁ∑§, •ı‚ÃøÊ‹ =

ß‚Á‹∞, {Æ =

•ı⁄U, ∑È§‹Á‹ÿÊªÿÊ‚◊ÿ =16060

ÉÊá≈U

= wÉÊá≈U ...(v)•’„U◊¬„U‹ËxÆkmÿÊòÊÊ◊¥⁄U‹ªÊ«∏UËmÊ⁄UÊÁ‹∞ªÿ‚◊ÿ∑§Ë•ı⁄UÁ»§⁄U•ª‹~ÆkmÿÊòÊÊ◊¥Á‹ÿªÿ‚◊ÿ∑§Ë•‹ª-•‹ªªáÊŸÊ

∑§⁄¥Uª(Œπ¥ÁøòÊ|)–(i)⁄U‹ÿÊòÊÊ∑§¬„U‹÷Êª∑§Á‹∞,„U◊Ê⁄U¬Ê‚„ÒU— ÿÊòÊÊ = xÆkm/h ŒÍ⁄UË = xÆkm•ı⁄U, ‚◊ÿ = ?(ªáÊŸÊ∑§⁄UŸÊ„ÒU)

•’, øÊ‹ =

ß‚Á‹∞, xÆ =

•ı⁄U, Á‹ÿÊªÿÊ‚◊ÿ =3030

ÉÊá≈U

= vÉÊá≈UÊ ...(w)

ÁøòÊ |. Ÿ◊ÍŸÊÕ¸‚◊SÿÊy∑§Á‹∞⁄UπÊÁøòÊ–

(ii)⁄U‹-ÿÊòÊÊ∑§ŒÍ‚⁄U÷Êª∑§Á‹∞,„U◊◊ÊŸ‹Ã„Ò¥UÁ∑§⁄U‹ªÊ«∏UË∑§ËøÊ‹x km/h„ÒU–ß‚Á‹∞,⁄U‹-ÿÊòÊÊ∑§ŒÍ‚⁄U÷Êª∑§Á‹∞,„U◊Ê⁄U¬Ê‚„ÒU—

øÊ‹ = x km/h(◊ÊŸË„ÈUß¸) ŒÍ⁄UË = ~Ækm•ı⁄U, ‚◊ÿ = ?(ªáÊŸÊ∑§⁄UŸÊ„ÒU)

•’, øÊ‹ =

ß‚Á‹∞, x =

•ı⁄U, Á‹ÿÊªÿÊ‚◊ÿ =90x

ÉÊá≈U ...(x)

•’,‚◊Ë∑§⁄UáÊ(w)•ı⁄U(x)∑§Ù¡Ù«∏U∑§⁄U,„U◊‚ê¬ÍáÊ¸ÿÊòÊÊ◊¥Á‹ÿÊªÿÊ‚◊ÿ¬˝Ê#∑§⁄U‹Ã„Ò¥U–

∑È§‹Á‹ÿÊªÿÊ‚◊ÿ = v+90x

ÉÊá≈U ...(y)

xfr 13

‚◊Ë∑§⁄UáÊ(v)‚,„U◊¬„U‹‚„UË¡ÊŸÃ„Ò¥UÁ∑§¬ÍáÊ¸ÿÊòÊÊ◊¥Á‹ÿÊªÿÊ∑È§‹‚◊ÿwÉÊá≈UÊ„ÒU–ß‚Á‹∞,‚◊Ë∑§⁄UáÊ(y)•ı⁄U(v)∑§ËÃÈ‹ŸÊ∑§⁄UŸ¬⁄U,„U◊¬ÊÃ„Ò¥U—

v+90x

= w

90x

= w–v

90x

= v

•ı⁄U, x = ~Ækm/h

•Ã—,⁄U‹ªÊ«∏UË∑§Ù•ª‹~Ækm∑§ËŒÍ⁄UË∑§Ù~Ækm/h∑§ËøÊ‹‚Ãÿ∑§⁄UŸÊøÊÁ„U∞–Ÿ◊ÍŸÊÕ¸ ‚◊SÿÊ z. ∞∑§⁄U‹ªÊ«∏UËÆ.zwÉÊ¢≈UÃ∑§{Ækm/h∑§ËøÊ‹‚,•ª‹Æ.wyÉÊ¢≈UÃ∑§xÆkm/h∑§ËøÊ‹‚•ı⁄UÁ»§⁄U•ª‹

Æ.|vÉÊ¢≈UÃ∑§|Ækm/h∑§ËøÊ‹‚ø‹ÃË„ÒU–⁄U‹ªÊ«∏UË∑§Ë•ı‚ÃøÊ‹ÄÿÊ„ÒU?„U‹ — ß‚‚◊SÿÊ◊¥,‚’‚¬„U‹„U◊¥øÊ‹•ı⁄U‚◊ÿ∑§ËÃËŸÁ÷ãŸ-Á÷ãŸÁSÕÁÃÿÙ¥◊¥⁄U‹ªÊ«∏UËmÊ⁄UÊø‹ËªÿËŒÍÁ⁄UÿÙ¥∑§ËªáÊŸÊ∑§⁄UŸË„ÒU–

(i) ¬„U‹ËÁSÕÁÃ◊¥,⁄U‹ªÊ«∏UËÆ.zwÉÊá≈U∑§‚◊ÿÃ∑§{Ækm/h∑§ËøÊ‹‚ø‹ÃË„ÒU–

•’, øÊ‹ =

ß‚Á‹∞, {Æ =

•ı⁄U, ŒÍ⁄UË = {Æ×Æ.zw = xv.wkm ...(v) (ii) ŒÍ‚⁄UËÁSÕÁÃ◊¥,⁄U‹ªÊ«∏UËÆ.wyÉÊá≈U∑§‚◊ÿÃ∑§xÆkm/h∑§ËøÊ‹‚ø‹ÃË„ÒU–

•’, øÊ‹ =

ß‚Á‹∞, xÆ =

•ı⁄U, ŒÍ⁄UË = xÆ×Æ.wy = |.wkm ...(w) (iii) ÃË‚⁄UËÁSÕÁÃ◊¥,⁄U‹ªÊ«∏UËÆ.|vÉÊá≈U∑§‚◊ÿÃ∑§|Ækm/h∑§ËøÊ‹‚ø‹ÃË„ÒU–

¬ÈŸ—, øÊ‹ =

ß‚Á‹∞, |Æ =

•ı⁄U, ŒÍ⁄UË = |Æ×Æ.|v = y~.|km ...(x)

•’,‚◊Ë∑§⁄UáÊ(v),(w)•ı⁄U(x)‚,„U◊¬ÊÃ„Ò¥U—

∑È§‹ø‹ËªÿËŒÍ⁄UË = xv.w+|.w+y~.|

= }}.vkm ...(y)

•ı⁄U, ∑È§‹Á‹ÿÊªÿÊ‚◊ÿ = Æ.zw+Æ.wy+Æ.|v

= v.y|h ...(z)

„UU◊¡ÊŸÃ„Ò¥UÁ∑§— •ı‚ÃøÊ‹ =


9 1

Publisher : SChand Publications ISBN : 9789385676659Author : Lakhmir Singh AndManjit Kaur

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