rotational motion (practice problem) - copy (3).doc

8/11/2019 Rotational Motion (Practice Problem) - Copy (3).doc

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Problems based on centre of mass1. Where will be the centre of mass on combining two masses m and M (M> m )

(a) Towards m (b) Towards M (c) Between m and M (d) Anywhere

2. Two objects of masses 200 gm and 500 gm possess elocities i!"0 m/s and ji !5!# + m/s respecti ely$ The

elocity of their centre of mass in m/s is(a) ji !25!5 (b) ji !25!

%5

(c) ji !%

25!5 + (d) ji !%5!25

3. &n theHCl molec'le the separation between the n'clei of the two atoms is abo't "$2% (" * "0 +"0 m )$ Theappro,imate location of the centre of mass of the molec'le from hydrogen is (ass'ming the chlorine atom to beabo't #5$5 times massi e as hydrogen)

(a) " (b) 2$5 (c) "$2- (d) "$5 4. .o'r particle of masses m 2 m # m and - m are arranged at the corners of a parallelogram with each side e/'al

to a and one of the angle between two adjacent sides is 0 o$ The parallelogram lies in the x 1 y plane with mass mat the origin and - m on the x 1a,is$ The centre of mass of the arrangement will be located at

(a)

aa 5$0

2# (b)

aa

-#

5$0 (c)

2(

-

# aa (d)

-#

2aa

5. A system consists of # particles each of mass m and located at (" ") (2 2) (# #)$ The co1ordinate of the centreof mass are(a) ( ) (b) (# #) (c) (2 2) (d) (" ")

6. &f a bomb is thrown at a certain angle with the hori3ontal and after e,ploding on the way the di4erent fragmentsmo e in di4erent directions then the centre of mass(a) Wo'ld mo e along the same parabolic path (b) Wo'ld mo e along a hori3ontal path(c) Wo'ld mo e along a ertical line (d) one of these

7. .o'r identical spheres each of mass m are placed at the corners of s/'are of side 2 metre $ Ta6ing the point of

intersection of the diagonals as the origin the co1ordinates of the centre of mass are(a) (0 0) (b) (" ") (c) (+ " ") (d) (" + ")

8. Two particles A and B initially at rest mo e towards each other 'nder a m't'al force of attraction$ At the instantwhen the speed of A is v and the speed of B is 2v the speed of centre of mass of the system is

[IIT-JEE 1982]

(a) 7ero (b) v (c) "$5v (d) # v 9. A circ'lar plate of 'niform thic6ness has diameter 5 cm $ A circ'lar part of diameter -2 cm is remo ed from one

edge$ What is the position of the centre of mass of the remaining part(a) # cm (b) cm (c) cm (d) "2 cm

10. Two point masses m and M are separated by a distance L$ The distance of the centre of mass of the system fromm is

(a) )8( MmL (b) )8( mML (c)

+ MmML (d)

+ MmmL

11. Three identical spheres each of mass " kg are placed to'ching each other with their centres on a straight line$ Their centres are mar6ed K, L and M respecti ely$ The distance of centre of mass of the system from K is

(a)#

LMKMKL ++ (b)#

KMKL + (c)#

LMKL + (d)#

LMKM +

12. Two particles of masses " kg and # kg mo e towards each other 'nder their m't'al force of attraction$ o otherforce acts on them$ When the relati e elocity of approach of the two particles is 2 m/s, their centre of mass hasa elocity of 0$5 m/s. When the relati e elocity of approach becomes # m/s, the elocity of the centre of mass is(a) 0$5 m/s (b) 0$%5m 8s (c) "$25 m 8s (d) 7ero

Problems based on angular displacement, velocity and acceleration


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13. &n rotational motion of a rigid body all particle mo e with(a) 9ame linear and ang'lar elocity (b) 9ame linear and di4erent ang'lar elocity(c) With di4erent linear elocities and same ang'lar elocities (d) With di4erent linear

elocities and di4erent ang'lar elocities14. The ang'lar speed of a :y+wheel ma6ing "20 re ol'tion8 minute is

(a) rad/sec (b) 2 rad/sec (c) - rad/sec (d) - 2

rad/sec15. A :ywheel gains a speed of 5-0 r.p.m. in sec $ &ts ang'lar acceleration will be

(a) # rad/sec 2 (b) rad/sec 2 (c) "; rad/sec 2 (d) 5- rad/sec 2

16. A car is mo ing at a speed of %2 km/hr $ the diameter of its wheels is 0$5 m $ &f the wheels are stopped in 20rotations by applying bra6es then ang'lar retardation prod'ced by the bra6es is

(a) + 25$5 rad/s 2 (b) + 2 $5 rad/s 2 (c) + ##$5 rad/s 2 (d) + -5$5 rad/s 2

17. A wheel is rotating at 00 r.p.m. abo't its a,is$ When the power is c't1o4 it comes to rest in " min'te$ Theang'lar retardation in radian/s 2 is

(a) 2 (b) - (c) (d) ;

18. A particle B is mo ing in a circle of radi's a with a 'niform speed u $ C is the centre of the circle and AB isdiameter$ The ang'lar elocity of B abo't A and C are in the ratio

(a) " < " (b) " < 2 (c) 2 < " (d) - < "19. Two particles ha ing mass = M= and =m = are mo ing in circ'lar paths ha ing radii and r $ &f their time periods are

same then the ratio of their ang'lar elocities will be[CBSE PM/PD 2001]

(a) r (b)r

(c) " (d)r

20. A body is in p're rotation$ The linear speed v of a particle the distance r of the particle from the a,is and

ang'lar elocity of the body are related as r v

= th's

(a)r "

(b) r (c) 0= (d) is independent of r

21. A strap is passing o er a wheel of radi's #0 cm $ 'ring the time the wheel mo ing with initial constant elocityof 2 re 8sec$ comes to rest the strap co ers a distance of 25 m $ The deceleration of the wheel in rad 8s 2 is(a) 0$ - (b) "$2 (c) 2$0 (d) 2$5

22. A particle starts rotating from rest$ &ts ang'lar displacement is e,pressed by the following e/'ationt t "$0025$0 2 = where is in radian and t is in seconds$ The ang'lar acceleration of the particle is

(a) 0$5 rad 8sec ! at the end of "0 sec (b) 0$# rad8sec 2 at the end of 2 sec(c) 0$05 rad 8sec ! at the end of " sec (d) ?onstant 0$05 rad 8sec !

23. The planes of two rigid discs are perpendic'lar to each other$ They are rotating abo't their a,es$ &f their ang'larelocities are # rad 8sec and - rad 8sec respecti ely then the res'ltant ang'lar elocity of the system wo'ld be

(a) " rad 8sec (b) % rad 8sec (c) 5 rad 8sec (d) "2 rad 8sec

24. A sphere is rotating abo't a diameter(a) The particles on the s'rface of the sphere do not ha e any linear acceleration(b) The particles on the diameter mentioned abo e do not ha e any linear acceleration

a (c) i4erent particles on the s'rface ha e di4erent ang'lar speeds(d) All the particles on the s'rface ha e same linear speed

25. A rigid body is rotating with ariable ang'lar elocity )( "t a at any instant of time t. The total angles'btended by it before coming to rest will be ( a and " are constants)

(a)2

)( a"a (b)"

a2

2(c)

""a

2

22 (d)a

"a2

22


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26. When a ceiling fan is switched on it ma6es "0 rotations in the @rst # seconds$ ow many rotations will it ma6e inthe ne,t # seconds (Ass'me 'niform ang'lar acceleration)(a) "0 (b) 20 (c) #0 (d) -0

27. When a ceiling fan is switched o4 its ang'lar elocity falls to half while it ma6es # rotations$ ow many morerotations will it ma6e before coming to rest (Ass'me 'niform ang'lar retardation)(a) # (b) 2- (c) "; (d) "2

28. et A be a 'nit ector along the a,is of rotation of a p'rely rotating body andB be a 'nit ector along the

elocity of a particle # of the body away from the a,is$ The al'e of B A $ is

(a) " (b) + " (c) 0 (d) one of these

Problems based on torque, couple Basic level

29. et $ be the force acting on a particle ha ing position ector % ar nd be the tor/'e of this force abo't theorigin$ Then [AIEEE 2003](a) 0$and0$ == % $ % r (b)

0$and0$ = % $ % r

(c) 0$and0$ = % $ % r (d)0$and0$ % $ % r

30. A co'ple prod'ces [CBSE PMT 1997](a) C'rely linear motion (b) C'rely rotational motion(c) inear and rotational motion (d) o motion

31. .or a system to be in e/'ilibri'm the tor/'es acting on it m'st balance$ This is tr'e only if the tor/'es are ta6enabo't(a) The centre of the system (b) The centre of mass of the

system(c) Any point on the system (d) Any point on the system oro'tside it

32. What is the tor/'e of the force &k ji$ )!-!#!2( += acting at the pt$ mk jir )!#!2!#( ++=

abo't the origin

(a) k ji !"#!!"% ++ (b) k ji !"2!! + (c)k ji !"#!0!"% (d) k ji !"2!! +

33. Two men are carrying a 'niform bar of length L on their sho'lders$ The bar is held hori3ontally s'ch thatyo'nger man gets th)-8"( load$ 9'ppose the yo'nger man is at the end of the bar what is the distance of theother man from the end(a) #8L (b) 28L (c) #82 L (d) -8# L

34. A 'niform meter scale balances at the cm-0 mar6 when weights of g"0 and g20 are s'spended from thecm"0 and cm20 mar6s$ The weight of the metre scale is

(a) g50 (b) g0 (c) g%0 (d) g;0

Advance level

35. A c'bical bloc6 of side L rests on a ro'gh hori3ontal s'rface with coeDcient of friction $ A hori3ontal force $ isapplied on the bloc6 as shown$ &f the coeDcient of friction is s'Dciently high so that the bloc6 does not slidebefore toppling the minim'm force re/'ired to topple the bloc6 is

[IIT-JEE (Scree ! "# 2000]

(a) &n@nitesimal

(b) mg 8-

(c) mg 82

L

$


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(d) mg )"(

36. When a force of $0 & is e,erted at '#0 to a wrench at a distance of ; cm from the n't it is j'st able to loosenthe n't$ What force $ wo'ld be s'Dcient to loosen it if it acts perpendic'larly to the wrench at " cm from then't

(a) # & (b) &

(c) - &

(d) "$5 &

37. A person s'pports a boo6 between his @nger and th'mb as shown (the point of grip is ass'med to be at thecorner of the boo6)$ &f the boo6 has a weight of ( then the person is prod'cing a tor/'e on the boo6 of

(a)2a( anticloc6wise

(b) 2"

( anticloc6wise(c) (a anticloc6wise

(d) (a cloc6wise

38. Weights of ggg "00$$$$$(2(" are s'spended from the " cm 2 cm $$$$$$ "00cm mar6s respecti ely of a lightmetre scale$ Where sho'ld it be s'pported for the system to be in e/'ilibri'm(a) 55 cm mar6 (b) 0 cm mar6 (c) cm mar6 (d) %2 cm mar6

39. A 'niform c'be of side a and mass m rests on a ro'gh hori3ontal table$ A hori3ontal force $ is applied normal to

one of the faces at a point that is directly abo e the centre of the face at a height-

# a abo e the base$ The

minim'm al'e of $ for which the c'be begins to tilt abo't the edge is (ass'me that the c'be does not slide)

(a)-

mg (b)#

2 mg (c)-

# mg (d) mg

Problems based on moment of inertia

Basic level

40. A circ'lar disc of radi's and thic6ness has moment of inertia ) abo't an a,is passing thro'gh its centre

and perpendic'lar to its plane$ &t is melted and recasted into a solid sphere$ The moment of inertia of thesphere abo't its diameter as a,is of rotation is

[EAMCET 2003]

(a) ) (b);

2 ) (c)5

) (d)"0

)

41. The moment of inertia of a meter scale of mass 0$ kg abo't an a,is perpendic'lar to the scale and located atthe 20 cm position on the scale in kg m 2 is (Breadth of the scale is negligible)

[EAMCET 2003]

(a) 0$0%- (b) 0$"0- (c) 0$"-; (d) 0$20;42. Two discs of the same material and thic6ness ha e radii 0$2 m and 0$ m $ Their moments of inertia abo't their

a,es will be in the ratio [MP PET 2003](a) " < ;" (b) " < 2% (c) " < (d) " < #

43. A circ'lar disc is to be made by 'sing iron and al'mini'm so that it ac/'ires ma,im'm moment of inertia abo'tits geometrical a,is$ &t is possible with

[CBSE PMT 2002]

(a) &ron and al'mini'm layers in alternate order (b) Al'mini'm at interior and iron s'rro'nding it(c) &ron at interior and al'mini'm s'rro'nding it (d) Either (a) or (c)

44. The moment of inertia of semicirc'lar ring abo't its centre is[AIEEE 2002]

;cm

;cm

#0 o

$ &

"

a


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(a) M 2 (b)2

2M (c)-

2M (d) one of these

45. Foment of inertia of a disc abo't its own a,is is )$ &ts moment of inertia abo't a tangential a,is in its plane is [MPPMT 2002]

(a) )25

(b) # ) (c) )2#

(d) 2 )46. A wheel of mass "0 kg has a moment of inertia of " 0 kg +m 2 abo't its own a,is the radi's of gyration will be

[P$. PMT 2001]

(a) "0 m (b) ; m (c) m (d) - m47. .o'r particles each of mass m are placed at the corners of a s/'are of side length l$ The radi's of gyration of the

system abo't an a,is perpendic'lar to the s/'are and passing thro'gh its centre is[EAMCET (Me%.# 2000]

(a)2

l (b)

2l (c) l (d) l)2(

48. The moment of inertia of a rod (length l mass m ) abo't an a,is perpendic'lar to the length of the rod andpassing thro'gh a point e/'idistant from its mid point and one end is

[MP PMT 1999]

(a)"2

2ml (b) 2-;%

ml (c) 2-;

"#ml (d) 2

-;

"ml

49. Three point masses #2" mmm are located at the ertices of an e/'ilateral triangle of length ==a $ Themoment of inertia of the system abo't an a,is along the altit'de of the triangle passing thro'gh "m is

[&'r ' ' CEE 1996]

(a)-

)(2

#2a

mm + (b) 2#2" )( ammm ++ (c) 2)(2

2"a

mm + (d) 2#2 )( amm +

50. &n a rectangle )2( ABBC ABC* = $ The moment of inertia along which a,is will be minim'm[CBSE PMT 1993]

(a) BC

(b) B*

(c) H$

(d) +,

51. Two loops # and - are made from a 'niform wire$ The radii of # and - are "r and 2r respecti ely and

their moments of inertia are ") and 2) respecti ely$ &f -"2 =)) then"

2

r r

e/'als

[CPMT 1992]

(a) #82- (b) #8"- (c) #82- (d) #8"-

52. The moment of inertia of a sphere (mass M and radi's ) abo't it=s diameter is ) $ .o'r s'ch spheres arearranged as shown in the @g're$ The moment of inertia of the system abo't a,is = .. will be

(a) # )

(b) 5 )

(c) % )

(d) )

53. Three identical thin rods each of length l and mass M are joined together to form a letter H$ What is the momentof inertia of the system abo't one of the sides of H

A B

* C

H $

+


6/17

(a)#

2Ml (b)-

2Ml (c)#

2 2Ml (d)#

- 2Ml

54. Foment of inertia of a sphere of mass M and radi's is )$ Geeping M constant if a graph is plotted between )and then its form wo'ld be

(a) (b) (c) (d)

55. Three particles are sit'ated on a light and rigid rod along / a,is as shown in the @g're$ &f the system is rotatingwith an ang'lar elocity of sec82 rad abo't . a,is then the total 6inetic energy of the system is

(a) 2 0(b) ";- 0(c) 2% 0(d) - 0

56. Hn acco'nt of melting of ice at the north pole the moment of inertia of spinning earth

(a) &ncreases (b) ecreases (c) Iemains 'nchanged (d) epends on the time

57. According to the theorem of parallel a,es 2Md )) g += the graph between ) and d will be

(a) (b) (c) (d)

58. What is the moment of inertia of a s/'are sheet of side l and mass per 'nit area abo't an a,is passingthro'gh the centre and perpendic'lar to its plane

(a)"2

2l (b)2l (c)

"2

-l (d)-l

59. The adjoining @g're shows a disc of mass M and radi's lying in the 1 plane with its centre on . a,is at adistance a from the origin$ Then the moment of inertia of the disc abo't the 1a,is is

(a)

2

2

M

(b)

-

2

M

(c)

+ 22

-aM

(d)

+ 22

2aM

60. We ha e two spheres one of which is hollow and the other solid$ They ha e identical masses and moment of inertia abo't their respecti e diameters$ The ratio of their radi's is gi en by(a) %


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a,is the al'e of n is (diameter of the wire is ery m'ch smaller than r or nr )[EAMCET 2001]

(a) ; (b) (c) - (d) 2

62. Hne /'arter sector is c't from a 'niform circ'lar disc of radi's $ This sector has mass M$ &t is made to rotateabo't a line perpendic'lar to its plane and passing thro'gh the centre of the original disc$ &ts moment of inertia

abo't the a,is of rotation is[IIT-JEE (Scree ! "# 2001]

(a) 22"

M

(b) 2-"

M

(c) 2;"

M

(d) 22 M

63. Two discs of same thic6ness b't of di4erent radii are made of two di4erent materials s'ch that their masses aresame$ The densities of the materials are in the ratio " < #$ The moments of inertia of these discs abo't therespecti e a,es passing thro'gh their centres and perpendic'lar to their planes will be in the ratio

[)**r+ee 2000]

(a) " < # (b) # < " (c) " < (d) < "

64. A thin wire of length L and 'niform linear mass density is bent into a circ'lar loop with centre at 2 as shown$ The moment of inertia of the loop abo't the a,is is [IIT-JEE (Scree ! "#2000]

(a)2

#

; L

(b)2

#

" L

(c)2

#

"

5

L

(d)2

#

;

#

L

65. &f solid sphere and solid cylinder of same radi's and density rotate abo't their own a,is the moment of inertia will be greater for ( L * )

[)PMT 2000]

(a) 9olid sphere (b) 9olid cylinder (c) Both (d) E/'al both

66. Two point masses of 0$# kg and 0$% kg are @,ed at the ends of a rod of length "$- m and of negligible mass$ Therod is set rotating abo't an a,is perpendic'lar to its length with a 'niform ang'lar speed$ The point on the rodthro'gh which the a,is sho'ld pass in order that the wor6 re/'ired for rotation of the rod is minim'm is locatedat a distance of [IIT-JEE 1995, AIIMS 2000]

(a) 0$- m from mass of 0$# kg (b) 0$ ; from mass of 0$# kg

(c) 0$%0m from mass of 0$% kg (d) 0$ ; m from mass of 0$%kg

67. A circ'lar disc A of radi's r is made from an iron plate of thic6ness t and another circ'lar disc B of radi's - r ismade from an iron plate of thic6ness t 8-$ The relation between the moments of inertia A) and B) is

(a) B A )) > (b) B A )) =

0 o

0 o

2


8/17

(c) B A )) < (d) epends on the act'alal'es of t and r

68. A thin wire of length l and mass M is bent in the form of a semi1circle$ What is its moment of inertia abo't an a,ispassing thro'gh the ends of the wire

(a)2

2Ml (b)2

2

Ml (c)2

22

Ml (d)2

2

2

Ml

69. &f)" is the moment of inertia of a thin rod abo't an a,is perpendic'lar to its length and passing thro'gh its centreof mass and )2 is the moment of inertia of the ring formed by bending the rod then

(a) )"


9/17

76. Two rigid bodies A and B rotate with rotational 6inetic energies +A and +B respecti ely$ The moments of inertia of A and B abo't the a,is of rotation are )A and )B respecti ely$ &f )A * )B8- and +A * "00 +B the ratio of ang'larmoment'm ( LA) of A to the ang'lar moment'm ( LB) of B is

[JIPME) 2001 02]

(a) 25 (b) 58- (c) 5 (d) "8-

77. A 'niform hea y disc is rotating at constant ang'lar elocity abo't a ertical a,is thro'gh its centre andperpendic'lar to the plane of the disc$ et L be its ang'lar moment'm$ A l'mp of plasticine is droppedertically on the disc and stic6s to it$ Which will be constant

[AM (Me%.# 2001]

(a) (b) and L both (c) L only (d) either nor L

78. An e/'ilateral triangle ABC formed from a 'niform wire has two small identical beads initially located at A$ Thetriangle is set rotating abo't the ertical a,is A2 $ Then the beads are released from rest sim'ltaneo'sly andallowed to slide down one along AB and the other along AC as shown$ eglecting frictional e4ects the/'antities that are conser ed as the beads slide down are


(a) Ang'lar elocity and total energy (6inetic and potential)

(b) Total ang'lar moment'm and total energy

(c) Ang'lar elocity and moment of inertia abo't the a,is of rotation(d) Total ang'lar moment'm and moment of inertia abo't the a,is of rotation

79. A thin circ'lar ring of mass M and radi's r is rotating abo't its a,is with a constant ang'larelocity $ Two objects each of mass m are attached gently to the opposite ends of a diameter of the ring$ The ring will now rotate with an ang'lar elocity

[IIT-JEE 1983, MP PMT 1994 97 98, CBSE PMT 1998, B& 1998, MP PET 1998 99]

(a) mMmM

2)2(

+

(b) mMM

2+

(c) mMM

+

(d) MmM )2( +

80. The earth + mo es in an elliptical orbit with the s'n 4 at one of the foci as shown in the @g're$ &ts speed of motion will be ma,im'm at the point

[B& 1994]

(a) C

(b) A

(c) B

(d) *

81. A rigid spherical body is spinning aro'nd an a,is witho't any e,ternal tor/'e$ 'e to change in temperat're theol'me increases by "J$ &ts ang'lar speed

[AIIMS 1992]

(a) Will increase appro,imately by "J (b) Will decrease appro,imately by "J

(c) Will decrease appro,imately by 0$ %J (d) Will decrease appro,imately by 0$##J

82. A 'niform disc of mass M and radi's is rotating abo't a hori3ontal a,is passing thro'gh its centre withang'lar elocity $ A piece of mass m brea6s from the disc and :ies o4 ertically 'pwards$ The ang'lar speedof the disc will be

(a))()2(

mMmM

(b)

)()2(

mMmM

++ (c)

)()2(

mMmM

+ (d)

)()2(

mMmM

+

Advance level

A

B 2 C

g

A

*

B

C+

4


10/17

83. A particle 'ndergoes 'niform circ'lar motion$ Abo't which point on the plane of the circle will the ang'larmoment'm of the particle remain conser ed


(a) ?entre of the circle (b) Hn the circ'mference of the circle(c) &nside the circle (d) H'tside the circle

84. A thin 'niform circ'lar disc of mass M and radi's is rotating in a hori3ontal plane abo't an a,is passing thro'ghits centre and perpendic'lar to its plane with an ang'lar elocity $ Another disc of same dimension b't of mass M8- is placed gently on the @rst disc coa,ially$ The ang'lar elocity of the system now is

[IIT-JEE 1986, AIEEE 2002]

(a) 582 (b) 582 (c) 58- (d) 58-

85. A smooth sphere A is mo ing on a frictionless hori3ontal plane with ang'lar speed and center of mass withelocity v $ &t collides elastically and head1on with an identical sphere B at rest$ eglect friction e erywhere$After the collision their ang'lar speeds are A and B respecti ely$ Then


(a) A K B (b) A * B (c) A * (d) * B

86. A c'bical bloc6 of side a is mo ing with elocity v on a hori3ontal smooth plane as shown$ &t hits a ridge at point2 $ The ang'lar speed of the bloc6 after it hits 2 is


(a) # v 8-a

(b) # v 82a

(c)a

v

2

#

(d) 7ero

87. A stic6 of length l and mass M lies on a frictionless hori3ontal s'rface on which it is free to mo e in any way$ Aball of mass m mo ing with speed v collides elastically with the stic6 as shown in the @g're$ &f after the collisionball comes to rest then what sho'ld be the mass of the ball

(a) Mm 2=(b) Mm =(c) 28Mm =

(d) -8Mm =88. &n a playgro'nd there is a merry1go1ro'nd of mass "20 kg and radi's - m $ The radi's of gyration is # m $ A child of

mass #0 kg r'ns at a speed of 5 m 8sec tangent to the rim of the merry1go1ro'nd when it is at rest and then

j'mps on it$ eglect friction and @nd the ang'lar elocity of the merry1go1ro'nd and child(a) 0$2 rad 8sec (b) 0$" rad 8sec (c) 0$- rad 8sec (d) 0$; rad 8sec

Problems based on kinetic energy, work and power

Basic level

89. A ball rolls witho't slipping$ The radi's of gyration of the ball abo't an a,is passing thro'gh its centre of mass K $&f radi's of the ball be then the fraction of total energy associated with its rotational energy will be

[CBSE PMT 2003]

(a)2

2K (b)22

2

K

K

+

(c)22

2

K +(d)

2

22K +

90. &n a bicycle the radi's of rear wheel is twice the radi's of front wheel$ &f r $ r r and are the radii v . and v r arespeeds of top most points of wheel then

[ r! ' JEE 2003]

l

m

2

v

a

M


11/17

(a) v r * 2 v . (b) v . * 2 v r (c) v . * v r (d) v . > v r91. The total 6inetic energy of a body of mass "0 kg and radi's 0$5 m mo ing with a elocity of 2 m/s witho't

slipping is #2$; j'ule $ The radi's of gyration of the body is[MP PET 2003]

(a) 0$25 m (b) 0$2 m (c) 0$5 m (d) 0$- m

92. The moment of inertia of a body abo't a gi en a,is is 2$- kg5m2

$ To prod'ce a rotational 6inetic energy of %50 0an ang'lar acceleration of 5 rad/s 2 m'st be applied abo't that a,is for[B& 2002]

(a) sec (b) 5 sec (c) - sec (d) # sec93. A solid sphere of mass 500 gm and radi's "0 cm rolls witho't slipping with the elocity 20 cm/s $ The total 6inetic

energy of the sphere will be[P$. PMT 2002]

(a) 0$0"- 0 (b) 0$02; 0 (c) 2;0 0 (d) "-0 094. The ratio of rotational and translatory 6inetic energies of a sphere is [ CET (Me%.# 2001, A MC 2001]

(a)2

(b)%2

(c)52

(d)2%

95. A thin hollow cylinder open at both ends> which one wo'ld reach the bottom @rst(a) ?ylinder of radi's "r (b) ?ylinder of radi's 2r

0$" &

0$" &


14/17

(c) ?ylinder of radi's #r (d) All the three cylinders sim'ltaneo'sly

128. A solid cylinder of radi's and mass M rolls down on inclined plane witho't slipping and reaches the bottomwith a speed v $ The speed wo'ld be less than v if we 'se(a) A cylinder of same mass b't of smaller radi's (b) A cylinder of same mass b't of larger radi's(c) A cylinder of same radi's b't of smaller mass (d) A hollow cylinder of same mass and same radi's

129. A body starts rolling down an inclined plane of length L and height h $ This body reaches the bottom of the planein time t $ The relation between L and t is

(a) Lt (b) Lt 8" (c) 2Lt (d) 2"

Lt

130. A hollow cylinder is rolling on an inclined plane inclined at an angle of '#0 to the hori3ontal$ &ts speed aftertra elling a distance of "0 m will be(a) - m/sec (b) 0$%m/sec (c) %m/sec (d) 7ero

131. A solid sphere a solid cylinder a disc and a ring are rolling down an inclined plane$ Which of these bodies willreach the bottom sim'ltaneo'sly(a) 9olid sphere and solid cylinder (b) 9olid cylinder and disc(c) isc and ring (d) 9olid sphere and ring

132. A ball of radi's "" cm and mass ; kg rolls from rest down a ramp of length 2 m $ The ramp is inclined at '#5 tothe hori3ontal$ When the ball reaches the bottom its elocity is (sin #5 o * 0$5%)(a) 2 m 8s (b) 5 m 8s (c) - m 8s (d) m 8s

133. .rom an inclined plane a sphere a disc a ring and a shell are rolled witho't slipping$ The order of their reachingat the base will be(a) Iing shell disc sphere (b) 9hell sphere disc ring (c) 9phere disc shell ring(d) Iing sphere disc shell

134. A solid cylinder #0 cm in diameter at the top of an inclined plane 2$0 m high is released and rolls down theincline witho't loss of energy d'e to friction$ &ts linear speed at the bottom is(a) 5$2 m/sec (b) -$" M "0 # m/sec (c) 5" m/sec (d) 5" cm/sec

135. A cylinder of mass M and radi's rolls on an inclined plane$ The gain in 6inetic energy is

(a) 22" Mv (b) 2

2" ) (c) 2

-# Mv (d) 2

-# )

136. A disc of radi's is rolling down an inclined plane whose angle of inclination is &ts acceleration wo'ld be

(a) sin%5

g (b) sin#2

g (c) sin2

"g (d) sin

5

#g

137. A solid cylinder (i) rolls down (ii) slides down an inclined plane$ The ratio of the accelerations in these conditionsis(a) # < 2 (b) 2 < # (c) # < 2 (d) #


15/17

(a) g(b) g5

(c) g"0

(d) g#

143. A ring ta6es time "t in slipping down an inclined plane of length L and ta6es time 2t in rolling down the same

plane$ The ratio2

"

t t

is

(a) "


16/17

(a)M

$ 2

(b)M$

(c) M$

2

(d)M$

-149. A massless string is wrapped ro'nd a disc of mass M and radi's $ Another end is tied to a mass m which is

initially at height h from gro'nd le el as shown in the @g$ &f the mass is released then its elocity while to'chingthe gro'nd le el will be

(a) gh2

(b)mM

gh2

(c) Mmgh 82

(d) Mmmgh +28-

150. A cylinder of mass M and radi's r is mo'nted on a frictionless a,le o er a well$ A rope of negligible mass iswrapped aro'nd the cylinder and a b'c6et of mass m is s'spended from the rope$ The linear acceleration of theb'c6et will be

(a)mM

Mg2+

(b)Mm

Mg2

2

+

(c) mMMg

+2

(d)mM

mg2

2

+ Advance level

151. A 'niform solid cylinder of mass M and radi's rotates abo't a frictionless hori3ontal a,le$ Two similar massess'spended with the help two ropes wrapped aro'nd the cylinder$ &f the system is released from rest then theacceleration of each mass will be

(a)mM

mg2

-

+

(b)mM

mg-

-

+

(c)mM

mg+

2

(d)mM

mg2

2

+152. &n the abo e problem the ang'lar elocity of the cylinder after the masses fall down thro'gh distance h will be

M

mv

m

M

m

$

M

hm


17/17

(a) )-8(;"

mMmgh + (b) )8(;" mMmgh + (c) )8(" mMmgh + (d)

)28(;"

mMmgh +

Problems based on compound pendulum Basic level

153. A metre scale is s'spended ertically from a hori3ontal a,is passing thro'gh one end of it$ &ts time period wo'ldbe

(a) "$ - sec (b) 2 sec (c) 2$5 sec (d) #$2 sec154. A disc of radi's is made to oscillate abo't a hori3ontal a,is passing thro'gh its periphery$ &ts time period wo'ld

be

(a)g2

#2 (b)

g#2

2 (c)g

2 (d)g

22

Advance level

155. A solid c'be of side l is made to oscillate abo't a hori3ontal a,is passing thro'gh one of its edges$ &ts time periodwill be

(a)gl

#22

2 (b)gl

#2

2 (c)gl

2#

2 (d) gl

#

22

156. The string of a simple pend'l'm is replaced by a 'niform rod of length L and mass M$ &f the mass of the bob of the pend'l'm is m then for small oscillations its time period wo'ld be (ass'me radi's of bob r KK L)

(a)gmM

LmM

)2(#

)#(22

+

+ (b)

gmM

LmM

)#(#

)2(2

+

+ (c)

g

L

m

M

#

22 (d)

g

L

mM

mM

+

+#

2

rotational motion (practice problem) - copy (3).doc

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