CHAPTER 7 Rotation and Rolling Motion

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1. The moment of inertia of a body does not depend on *

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(a) the mass of the body

(b) the angular velocity of the body

(d) the distribution of the mass in the body

02. A uniform sphere of mass 500 g rolls without slipping on a plane surface so that its centre moves at a speed of 0.02 m/s *

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(a) 1.4 × 10-4 j

(b) 0.75 × 10-3 j

(d) 4.9 × 10-5 j

3. The moment of inertia of a metre stick of mass 300 gm, about an axis at right angles to the stick and located at 30 cm mark, is *

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(a) 8.3 × 105 g-cm2

(b) 5.8 g-cm2

(d) None of these

4. Four masses are fixed on a massless rod as shown in the figure. Q 0.2 m 0.2 m 0.2 m 0.2 m P 2 kg 5 kg 5 kg 2 kg The moment of inertia about the axis PQ is about *

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(a) 2 kg-m2

(b) 1.04 kg-m2

(d) 0.3 kg-m2

5. Three point masses m are placed at the vertices of an equilateral triangle of side a. Moment of inertia of the system about an axis COD passing through a mass m at O and lying in the plane of AOB and perpendicular to OA is *

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(a) 2ma2

(b) 2 /3 ma2

(d) 7 /4 ma2

6. Three thin rods each of length L and mass M are placed along x, y and z-axes in such a way that one end of each of the rods in at the origin. L O Y L L X 2 1 3 Z The moment of inertia of this system about z-axis is *

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(a) 2ML2 /3

(b) 4ML2 /3

(d) ML2 /3

7. Two uniform thin identical rods AB and CD each of mass M and length L are joined so as to form a cross as shown. The moment of inertia of the cross about a bisector line EF is *

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(a) ML2 /6

(b) ML2 /4

(c)ML2 / 12

(d) ML2 /3

8. Four identical rods are joined end to end to form a square. The mass of each rod is M. The moment of inertia of the square about the median line i *

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(a) Ml 2 /3

(b) Ml 2 /4

(c Ml 2 /6

(d) None of these

9. In the Q. 8, the moment of inertia of the system about one of the diagonals is *

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(a) 2M2 /3

(b) 13ML2 /3

(d) 13Ml2 /6

10. In the Q. 8, the moment of inertia of the system about an axis passing through the point of intersection of diagonals and perpendicular to the plane of the squa *

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(a) 4Ml2 /3

(b) 13Ml2 /3

(c)Ml 2 /6

(d) 13Mi2 /6

11. Three identical thin rods each of length l and mass M are joined together to form a letter H. The moment of inertia of the system about one of the sides of H is *

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(a) Ml 2/3

(b) Ml 2 /4

(d) 4Ml2 /3

12. Two rods OA and OB of equal length and mass are lying on XY-plane as shown in figure. Let Ix , Iy and Iz be the moments of inertia of both the rods about x, y and z-axis respectively. Then *

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(a) Ix = Iy> Iz

(b) Ix = Iy< Iz

(d) Iz> Iy > Ix

13. The moment of inertia of a uniform rod of length 2l and mass m about an axis xx′ passing through its centre and inclined at an angle α is *

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(a) ml 2/3,sin2α

(b) ml2/12,sin2α

(d) ml2/2,cos2α

14. Moment of inertia of a uniform circular disc about a diameter is I. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be *

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(a) 5I

(b) 3I

(d) 4I

15. Generally the mass of a fly wheel is concentrated in its rim. Why? *

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(a) To decrease the moment of inertia

(b) To increase the moment of inertia

(d) To obtain a strong wheel

16. Two rings of the same radius and mass are placed such that their centres are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to the plane of one of the rings is (mass of the ring = m, radius = r) *

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(a) (1/2) mr2

(b) mr2

(d) 2mr2

17. The diameter of a flywheel increases by 1%. What will be percentage increase in moment of inertia about axis of symmetry? *

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(a) 2%

(b) 4%

(d) 0.5%

18. Two circular discs A and B are of equal masses and thicknesses but made of metal with densities dA and dB (dA > dB). If their moments of inertia about an axis passing through their centres and perpendicular to circular faces be I A and I B, then *

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(a) I A=IB

(b) IA > IB

(d) IA ≥ I

19. Moment of inertia of a uniform annular disc of internal radius r and external radis R and mass M about an axis through its centre and perpendicular to its plane is *

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(a) 1/2 M(R2-r2)

(b) 1/2 M(R2+r2)

(d)1/2 m(R2 + r4)/2(R2 - r2)

20. A circular disc A of radius r is made from an iron plate of thickness t and another circular disc B of radius 4r and thickness t/4. The relation between moments of inertia I A and I B is *

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(a) IA > IB

(b) IA = IB

(d) Depends on the actual values of t and r

21 Two discs one of density 7.2 g/cm3 and the other of density 8.9 gm/cm3 , are of same mass and thickness. Their moments of inertia are in the ratio *

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(a) 8 9 /7.2

(b) 7.2 /8.9

(d) 1:(8.9 × 7.2)

22. Two circular discs are of the same thickness. The diameter of A is twice that of B. The moment of inertia of A as compared to that of B is *

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(a) twice as large

(b) four times as large

(d) 16 times as large

23. Two thin discs each of mass M and radius r metre are attached as shown in figure, to form a rigid body. The rotational inertia of this body about an axis perpendicular to the plane of disc B and passing through its centre is *

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(a) 2Mr2

(b) 3Mr2

(d) 5Mr2

24. A circular disc is to be made using iron and aluminium. To keep its moment of inertia maximum about a geometrical axis, it should be so prepared that *

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(a) aluminium at interior and iron surrounds it

(b) iron at interior and aluminium surrounds it

(d) sheet of iron is used at both external surfaces and aluminium sheet as inner material

25. A uniform disc of radius R lies in XY-plane with its centre at origin. Its moment of inertia about the axis x = 2R and y = 0 is equal to the moment of inertia about the axis y = d and z = 0, where d is equal to *

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(a) 4/3 R

(b) 17/ 2 R

(d) 15/2 R

26. A wire of mass m and length l is bent in the form of a quarter circle. The moment of inertia of this wire about an axis passing through the centre of the quarter circle and perpendicular to the plane of the quarter circle is approximately *

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(a) 0.6 ml2

(b) ml2

(d) 0.4 ml2

27. Two discs have same mass and same thickness. Their materials are of densities r1 and r2 . The ratio of their moments of inertia about central axis will be *

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(a) ρ1 ρ 2 :1

(b) 1 : ρ1 ρ2

(d) ρ2: ρ1

28. Four spheres of diameter 2a and mass M are placed with their centres on the four corners of a square of side b. Then the moment of inertia of the system about an axis along one of the sides of the square is *

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(a) 4/5 Ma2+2Mb2

(b) 8/5 Ma2+2Mb2

(d) 4/5 Ma2+4Mb2

29. The moment of inertia of a solid sphere about an axis passing through centre of gravity is 1 5 MR2 ; then its radius of gyration about a parallel axis at a distance 2R from first axis is *

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(a) 5R

(b) 22/5 R

(d) 12/5 R

30. A uniform cylinder has a radius R and length L. If the moment of inertia of this cylinder about an axis passing through its centre and normal to its circular face is equal to the moment of inertia of the same cylinder about an axis passing through its centre and normal to its length; then *

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(a) L = R

(b) L= 3/R

(d) L = 0

31. A cricket mat of mass 50 kg is rolled loosely in the form of a cylinder of radius 2 m. Now again it is rolled tightly so that the radius becomes 3 4 of original value; then the ratio of moment of inertia of mat in the two cases is *

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(a) 1 : 3

(b) 4 : 3

(d) 3 : 5

32. A closed tube partly filled with water lies in a horizontal plane. If the tube is rotated about perpendicular bisector, the moment of inertia of the sys *

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(a) increases

(b) decreases

(d) depends on sense of rotation

33. Two spheres each of mass M and radius R/2 are connected with a massless rod of length 2R as shown in the figure. R 2 A M B Q 2R P M R 2 The moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod is *

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(a) 21/5MR2

(b) 2/5MR2

(d) 5/21MR2

34. Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle q with AB. The moment of inertia of the plate about the axis CD is then equal to *

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(a) I

(b) I sin2 q

(d) I cos2 (q/2)

35. Figure shows a thin metallic triangular sheet ABC. The mass of the sheet is M. 90º C A l B l The moment of inertia of the sheet about side AC is *

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(a) Ml 2/18

(b) Ml 2/12

(d) Ml 2/4

36. Four holes of radius R are cut from a thin square plate of side 4R and mass M. The moment of inertia of the remaining portion about z-axis is *

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(a) π/12 MR2(b) 4

(B) (3 /-4- π/4)MR2

(B) (3 /-4- π/6)MR2

37. In a rectangle ABCD, AB = 2l and BC = l. Axes x-x and y-y pass through the centre of the rectangle. The moment of inertia is least about *

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(a) DB

(b) BC

(d) yy-axis

38. A uniform thin bar of mass 6m and length 12L is bent to make a regular hexagon. Its moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of the hexagon is *

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(a) 20mL2

(b) 6mL2

(d) 30mL2

39. A mass is revolving in a circle which is in the plane of paper. The direction of angular acceleration is *

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(a) upward the radius

(b) towards the radius

(d) at right angle to angular velocity

40. A constant torque acting on a uniform circular wheel changes its angular momentum from A0 to 4A0 in 4 seconds. The magnitude of this torque is *

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a) 3A0/4

(b) A0

(d) 12A0

41. A flywheel of mass 50 kg and radius of gyration about its axis of rotation of 0.5 m is acted upon by a constant torque of 12.5 N-m. Its angular velocity at t = 5 seconds is *

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(a) 2.5 rad/s

(b) 5 rad/s

(d) 10 rad/s

42. The moment of inertia of a body about a given axis is 1.2 kg × m2 . Initially, the body is at rest. In order to produce a rotational KE of 1500 joule, an angular acceleration of 25 rad/s must be applied about that axis for a duration of *

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(a) 4 seconds

(b) 2 seconds

(d) 10 seconds

43. A body having moment of inertia about its axis of rotation equal to 3 kg-m2 is rotating with angular velocity equal to 3 rad/s. Kinetic energy of this rotating body is the same as that of a body of mass 27 kg moving with a speed of *

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(a) 1.0 m/s

(b) 0.5 m/s

(d) 2.0 m/s

44. A body of moment of inertia of 3 kg × m2 rotating with an angular speed of 2 rad/sec has the same KE as a mass of 12 kg moving with a speed of *

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(a) 2 m/s

(b) 1 m/s

(d) 8 m/s

45. A spherical solid ball of 1 kg mass and radius 3 cm is rotating about an axis passing through its centre with an angular velocity of 50 rad/s. The kinetic energy of rotation is *

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(a) 4500 J

(b) 90 J

(d) (9/10) J

46. An electric fan has blades of length 30 cm as measured from the axis of rotation. If the fan is rotating at 1200 rpm, the acceleration of a point on the tip of a blade is about *

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(a) 4740 m/s2

(b) 5055 m/s2

(d) 2370 m/s2

47. A triangular plate of uniform thickness and density is made to rotate about an axis perpendicular to the plane of the paper and (a) passing through A, (b) passing through B, by the application of some force F at C (mid-point of AB) as shown in the figure. In which case angular acceleration is more? *

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(a) In case (a)

(b) In case (b)

(d) None of these

48. A uniform rod of mass M and length L is pivoted at one end such that it can rotate in a vertical plane. There is negligible friction at the pivot. The free end of the rod is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle θ with the vertical is *

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(a) g sinθ

(b) g /L sin θ

(d) 6gLsin θ

49. A thin hollow cylinder is free to rotate about its geometrical axis. It has a mass of 8 kg and a radius of 20 cm. A rope is wrapped around the cylinder. What force must be exerted along the rope to produce an angular acceleration of 3 rad/s2 ? *

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(a) 8.4 N

(b) 5.8 N

(d) None of these

50. A light string is wound several times around a spool of mass M and radius R. The free end of the string is attached to a fixed point and the spool is held so that the part of the string not in contact with it is vertical. If the spool is let go, the acceleration is *

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(a) g/3

(b) 2g/3

(d) 3g/4

51. A uniform metre stick of mass M is hinged at one end and supported in a horizontal direction by a string attached to the other end. What should be the initial acceleration (in rad/s2 ) of the stick if the string is cut? *

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(a) 3/2 g

(b) g

(d) 4g

52. A rigid body rotates about a fixed axis with variable angular velocity equal to a – bt at time t, where a and b are constants. The angle through which it rotates before it comes to rest is *

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(a) α2/2β

(B)α2-β2/2α

(c)α2- β2/2β

(d) α (α − β)/2

53. A uniform disc is acted by two equal forces of magnitude F. One of them, acts tangentially to the dis other one is acting at the central point of the disc. The friction between disc surface and ground surface is nF. If r be the radius of the disc, then the value of n would be (in N) *

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(a) 0

(b) 1.2

(d) 3.2

54. A wheel with an initial angular velocity wo reaches an angular velocity of 5wo while it turns through an angle of 6 rad. Its uniform angular acceleration a is *

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(a) 1/32 ωo rad/sec2

(b) 2/32 ωo rad/sec2

(d) 4 2 ωo rad/sec2

55. Two wheels are mounted side by side and each is marked with a dot on its rim. The two dots are aligned with the wheels at rest, then one wheel is given a constant angular acceleration of p/2 rad/s2 and the other p/4 rad/s2 . Then the two dots become aligned again for the first time after *

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(a) 2 seconds

(b) 4 seconds

(d) 8 seconds

56. If vector F be a force acting on a particle having the position vector r and τ be the torque of this force about the origin, then *

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(a) r~r~=0and F.r=0

(a) r~r~=0and F.r≠0

(a) r~r~≠0and F.r≠0

(a) r~r~≠0and F.r=0

57. The angular velocity of the body changes from w1 to w2 without applying torque but by changing moment of inertia. The initial radius of gyration to the final radius of gyration is *

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(a) w2:w1

(b) ω2/2: ω 2

(d) 1/w2; 1w1

58. A cubical block of mass M and edge a slides down a rough inclined plane of inclination θ with a uniform velocity. The torque of the normal force on the block about its centre has a magnitude *

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(a) zero

(b) Mga

(d)Mga sinθ/2

59. A cylinder of mass M, radius R is resting on a horizontal platform (which is parallel to XY-plane) with its axis fixed along the y-axis and free to rotate about its axis. The platform is given a motion in X-direction given by x = Acos wt. There is no slipping between the cylinder and platform. The maximum torque acting on the cylinder during its motion is *

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(a) 1/2 MRAω2

(b)MRAω2

(d) MRAw2 × coswt

60. A uniform cube of side a and mass m rests on a rough horizontal table. A horizontal force F is applied normal to one of the faces at a point that is directly above the centre of face, at a height 3 4 a above the base. The minimum value of F for which the cube begins to tilt about the edge is (Assume that the cube does not slide) *

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(a) mg

(b) 2mg/3

(d) mg

61. A small object of mass m is attached to a light string and made to rotate on a frictionless table in a circular path whose radius can be changed by pulling the other end of the string through the hole at the centre. If the initial and final values of the radius of the orbit, speed and angular velocities of the object are r1 , v1 , w1 and r2 , v2 , w2 respectively, then w2 /w1 is *

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(a) r1 /r2

(b) (r1/r2)2

(a) r2 /r1

62. A circular disc of moment of inertia of 0.1 kg-m2 and radius 0.1 m has a massless string passing around its circumference. Starting from rest, the disc acquires an angular velocity of 1 rev/sec in a time interval of 2 sec, when the string is pulled down by a force F. The force F is *

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(a) 2π N ⋅

(b) (p/2) N

(d) 0.1p N

63. Of the two eggs which have identical sizes, shapes and weights, one is raw and other is half boiled. The ratio between the moment of inertia of the raw to the half boiled egg about central axis is *

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(a) = 1

(b) > 1

(d) Not comparable

64. A bicycle is travelling northwards and so its angular momentum points towards west. In what direction should the cyclist apply a torque to turn left? *

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(a) West

(b) South

(d) North

65. A disc is rotating with an angular velocity ωo . A constant retarding torque is applied on it to stop the disc. The angular velocity becomes (wo /2) after n rotations. How many more rotations will it make before coming to rest? *

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(a) n

(b) 2n

(d) n/3

66. Two equal and opposite forces act on a rigid body at a certain distance. Then *

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a) the body is in equilibrium

(b) the body will rotate about its centre of mass

(d) the body cannot rotate about its centre of mass

67. A thin rod of mass m and length 2l is made to rotate about an axis passing through its centre and perpendicular to it. If its angular velocity changes from 0 to w in time t, the torque acting on it is *

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(a)ml2w/12t

(b) ml2w/3t

(c)ml2w/t

4ml2w/3t

68. Angular momentum of a body is defined as the product of *

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(a) mass and angular velocity.

(b) centripetal force and radius.

(d) moment of inertia and angular velocity

69. When a mass is rotating in a plane about a fixed axis, its angular momentum is directed along *

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(a) the radius.

(b) the tangent to the orbit.

(d) the axis of rotation

70. A particle is moving along a straight line parallel to x-axis with constant velocity. Its angular momentum about the origin *

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(a) decreases with time.

(b) increases with time.

(d) is zero.

71. A particle of mass m = 5 units is moving with a uniform speed v = 3 2m in the XOY plane along the line Y = X + 4. The magnitude of the angular momentum of the particle about the origin is *

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(a) zero

(b) 60 unit

(d) 40 2 unit

72. When a torque acting upon a system is zero. Which of the following will be constant? *

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(a) Force

(b) Linear momentum

(d) Linear impulse

73. If a particle moves in the X-Y plane, the resultant angular momentum ha *

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(a) only x-component.

(b) only y-component.

(d) only z-component.

74. A particle of mass m is projected with a velocity v making an angle of 45 ° with the horizontal. The magnitude of angular momentum of the projectile about an axis of projection when the particle is at maximum height h is *

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(a) Zero

(b)mv2/4.014g

(c)mv2/.014g

(d) m 0.14gh

75. A ballet dancer, dancing on a smooth floor is spinning about a vertical axis with her arms folded with an angular velocity of 20 rad/s. When she stretches her arms fully, the spinning speed decreases to 10 rad/s. If I is the initial moment of inertia of the dancer, the new moment of inertia is *

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(a) 2I

(b) 3I

(d) I/3

76. Two bodies with moment of inertia I1 and I2 (I 1 > I2 ) have equal angular momentum. If the KE of rotation is E1 and E2 , then *

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(a) E1> E2

(b) E1< E2

(d) None of these

77. Angular momentum of the particle rotating with a central force is constant due to *

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(a) constant torque

(b) constant force

(d) zero torque

78. A particle of mass m moves with a constant velocity. Which of the following statements is not correct about its angular momentum about point O? *

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(a) It is zero when it is at A andmoving along OA.

(b) It is same at all points alongthe line DE.

(d) It increases as it moves along the line BC

79. A particle moves in a force field given by: F rF r = ˆ ( ),  where rˆ is a unit vector along the position vector  r, then which is true? *

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(a) The torque acting on the particle is not zero.

(b) The torque acting on the particle produces an angular acceleration in it.

(d) The angular momentum of the particle increases.

80. A solid cylinder, a circular disc, a solid sphere and a hollow cylinder of the same radius are placed on an inclined plane. Which of the following will have maximum acceleration at the bottom of the plane? *

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(a) Circular disc

(b) Solid cylinder

(d) Hollow cylinder

81. A 4 kg roller is attached to a massless spring of spring constant K = 100 N/m. It rolls without slipping along a frictionless horizontal road. The roller is displaced from its equilibrium position by 10 cm and then released. Its maximum speed will be *

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(a) 0.5 m/s

(b) 0.6 m/s

(d) 0.8 m/s

82. A uniform solid sphere rolls on a horizontal surface at 20 m/s. It then rolls up an incline having an angle of inclination at 30 ° with the horizontal. If the friction losses are negligible, the value of height h above the ground where the ball stops is *

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(a) 14.3 m

(b) 28.6 m

(d) 9.8 m

83. It is easier for a swimmer jumping into water from a height to describe a loop in the air by *

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(a) pulling the arms and legs closer

(b) spreading the arms and legs

(d) none of the given methods

84. When sand is poured on a rotating disc, its angular velocity will *

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(a) decrease

(b) increase

(d) None of these

85. The principle of conservation of angular momentum states that angular momentum *

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(a) always remains conserved

(b) is the product of moment of inertia and velocity

(d) None of the above

86. The angular momentum of a moving body remains constant if *

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(a) net external force is applied.

(b) net pressure is applied.

(d) net external torque is not applied.

87. A constant power is supplied to a rotating disc. Angular velocity (w) of disc varies with number of rotations (n) made by the disc as *

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(a) w ∝ (n)1/3

(b) w ∝ (n)3/2

(d) w ∝ (n)2

88. Given, ω = 2 ˆ k and r = + 2i 2 j ˆ ˆ. Find the linear velocity. *

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(a) 4 4 ˆ ˆ i j +

(b) 4 4 ˆ ˆ i k

(d) –4 4 ˆ ˆ

89. A circular platform is mounted on a vertical frictionless axle. Its radius is r = 2m and its moment of inertia is I = 200 kg-m2 . It is initially at rest. A 70 kg man stands on the edge of the platform and begins to walk along the edge at speed v0 = 10 m/s relative to the ground. The angular velocity of the platform is *

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(a) 1.2 rad/s

(b) 0.4 rad/s

(d) 0.7 rad/s

90. A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that moment of inertia of the system doubles. the kinetic energy of the system now is *

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(a) 2K

(b) K/2

(d) 4K

91. If a street light of mass M is suspended from the end of a uniform rod of length L in different possible patterns as shown in figure, then *

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(a) pattern A is more sturdy

(b) pattern B is more sturdy

(d) all will have same sturdiness

92. A horizontal platform is rotating with uniform angular velocity around the vertical axis passing through its centre. At some instant of time a viscous fluid of mass m is dropped at the centre and is allowed to spread out and finally fall. The angular velocity during this period *

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(a) decreases continuously

(b) decreases initially and increases again

(d) increases continuously

93. A raw egg and a hard boiled egg are made to spin on a table with the same angular speed about the same axis. The ratio of the time taken by the two to stop is *

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(a) = 1

(b) < 1

(d) None of these

94. A sphere cannot roll on *

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(a) a smooth horizontal surface

(b) a rough horizontal surface

(d) a rough inclined surface

95. A cylinder is rolling over a surface. Which points on it move rectilinearly? *

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(a) All points on the curved surface of the cylinder

(b) All points on the flat surfaces of the cylinder

(d) None of these

96. A hoop rolls on a horizontal ground without slipping with linear speed v. Speed of a particle P on the circumference of the hoop at angle q is
*

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(a) 2v sin θ/2

(b) v sinθv cos

(d) v cosθ

97. A horizontal platform is rotating with uniform angular velocity around the vertical axis passing through its centre. At some instant of time a viscous fluid of mass m is dropped at the centre and is allowed to spread out and finally fall. The angular velocity during this period *

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(a) decreases continuously

(b) decreases initially and increases again

(d) increases continuously

98. When a body rolls without sliding up an inclined plane, the frictional force is *

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(a) directed up the plane.

(b) directed down the plane.

(d) dependent on its velocity

99. The direction of the angular velocity vector is along *

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(a) the tangent to the circular path

(b) the inward radius

(d) the axis of rotation

100. A body rolls without slipping. The radius of gyration of the body about an axis passing through its centre of mass is k. If radius of the body be R, then the fraction of total energy associated with its rotational energy will be *

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(a) k2 R 2 +

(b) ( / ) 2 2 k R

(d) [ / R k( )

101. If a rigid body rolls on a surface without slipping, then *

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(a) angular speed is different at different points of arigid body

(b) linear speed is same at all points of the rigid body

(d) linear speed is maximum at the highest pointbut minimum at the point of contact

102. The angular momentum of a moving body remains constant if *

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(a) net external force is applied

(b) net external torque is applied

(d) net external torque is not applied

103. Three different balls of masses m1 , m2 and m3 are allowed to roll down from rest on three different frictionless paths OA, OB and OC respectively. Speeds v1 , v2 and v3 of masses m1 , m2 and m3 at the bottom of A, B and C are *

1 point

(a) (v1/m1) = (v2/m2) = (v3/m3)

(b) v1= v2 = v3

(d) v1> v2 > v3

104. A solid sphere rolls down two different inclined planes of the same height but of different inclinations *

1 point

(a) in both cases, the speeds and time of descent will be same.

(b) the speeds will be same but time of descent will be different.

(d) speeds and time of descent both will be different.

105. A disc and a hoop (ring) of the same mass and size roll down an inclined plane simultaneously. The object which reaches the bottom of the incline first is *

1 point

(a) hoop

(b) disc

(d) None of the above

106. A body of mass m slides down an incline and reaches the bottom with a velocity v. If the same mass was in the form of a ring which rolls down this incline, the velocity of the ring at the bottom would have been *

1 point

(a) v

(b) 2v

(d) ( / 2 5)v

107. Two identical solid cylinders run a race starting from rest at the top of an inclined plane. If one cylinder slides and the other rolls, then *

1 point

(a) the sliding cylinder will reach the bottom first with greater speed

(b) the rolling cylinder will reach the bottom first with greater speed

(d) both will reach the bottom simultaneously butwith different speeds

108. If a solid sphere, disc and cylinder are allowed to roll down an inclined plane from the same height *

1 point

(a) the cylinder will reach the bottom first

(b) the disc will reach the bottom first

(d) all will reach the bottom at the same time

109. One hollow and one solid cylinder of the same outer radius rolls down on a smooth inclined plane. The foot of the inclined plane is reached by *

1 point

(a) solid cylinder earlier

(b) hollow cylinder earlier

(d) the heavier earlier irrespective of being solid orhollow

110. An inclined plane makes an angle of 30° with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration equal to *

1 point

(a) g/3

(b) 5g/7

(d) 5g/14

111. A ring of mass 0.3 kg and radius 0.1 m and a solid cylinder of mass 0.4 kg and of the same radius are given the same KE and released simultaneously on a flat horizontal surface such that they begin to roll as soon as released towards a wall which is at the same distance from the ring and cylinder. Which will reach the wall first? *

1 point

(a) Ring

(b) Cylinder

(d) None of these

112. Two masses are attached to a rod end to end. If torque is applied they rotate with angular acceleration a. If their distances are doubled and same torque is applied, then they move with angular acceleration *

1 point

(a) 4a

(b) a

(d) a/4

113. A heavy disc is thrown on a horizontal surface in such a way that it slides with a speed Vo initially without rolling. It will start rolling without slipping when its speed reduces to *

1 point

(a) Vo/3

(b) 2v/3

(b) 3v/5

(d) 5v/7

114. A solid sphere and a hollow sphere of the same material and of same size can be distinguished without weighing *

1 point

(a) by determining their moments of inertia about their coaxial axes.

(b) by rolling them simultaneously on an inclined plane.

(d) by applying equal torques on them

115. A rod of length 1.4 m and negligible mass has two masses of 0.3 kg and 0.7 kg tied to its two ends. Find the location of the point on this rod where the rotational energy is minimum when the rod is rotated about that point *

1 point

(a) 0.98 m from 0.3 kg

(b) 0.98 m from 0.7 kg

(d) 0.7 m from 0.7 kg

116. A body can be negatively charged by *

1 point

(a) giving some protons to it

(b) removing some electrons from it

(d) removing some neutrons from it

117. When a sphere rolls without slipping, the ratio of its kinetic energy of translation to its total kinetic energy is *

1 point

(a) 1 : 7

(b) 1 : 2

(d) 5 : 7

118. If the equation for the displacement of a particle moving on a circular path is given by (q) = 2t 3 + 0.5 where q is in radians and t in seconds, then the angular velocity of the particle at t = 2 seconds, *

1 point

(a) 24 rad/s

(b) 12 rad/s

(d) 36 rad/s

119. If the radius of the earth is suddenly contracts to half of its present value, then the duration of day will be of *

1 point

(a) 6 hours

(b) 12 hours

(d) 24 hours

120. A particle of mass m is rotating in a plane in circular path of radius r. Its angular momentum is L. The centripetal force acting on the particle is *

1 point

(a) L2/mr

(b) L2m/r

(d) L2/mr3

121. When the axis of rotation passes through its centre of gravity, then the moment of inertia of a rigid body is *

1 point

(a) reduced to its minimum value

(b) zero

(d) infinity

122. The mass moment of inertia, of a body depends upon *

1 point

(a) angular velocity of the body

(b) angular acceleration of the body

(d) distribution of mass and axis of rotation.

123. If there is a change of angular momentum from J to 4J in 4 seconds, then torque, is *

1 point

(a) 0.75 J

(b) 3/4 J

(d) 4/3 J

124. For which of the following does the centre of mass lie outside the body? *

1 point

(a) A pencil

(b) A shotput

(d) A bangle

125. Which of the following points is the likely position of the centre of mass of the system as shown in below figure? nd R/2 R/2 sphere Air A B C D *

1 point

(a) A

(b) B

(d) D

126. A particle of mass m is moving in yz-plane with a uniform velocity v with its trajectory running parallel to +ve y-axis and intersecting z-axis at z = a as shown in below figure. The change in its angular momentum about the origin as it bounces elastically from a wall at y = constant is: *

1 point

(a) mva eˆx

(b) 2mva eˆx

(d) 2ymv eˆx

127. When a disc rotates with uniform angular velocity, which of the following is not true? *

1 point

(a) The sense of rotation remains same.

(b) The orientation of the axis of rotation remains same.

(d) The angular acceleration is non-zero and remains same

128. A uniform square plate has a small piece Q of an irregular shape removed and glued to the centre of the plate leaving a hole behind as shown in below figure. The moment of inertia about the z-axis is then *

1 point

(a) increased

(b) decreased

(d) changed in unpredicted manner.

129. In previous problem, the CM of the plate is now in the following quadrant of x-y plane, *

1 point

(a) I

(b) II

(d) IV

130. A Merry-go-round, made of a ring-like platform of radius R and mass M, is revolving with angular speed ω. A person of mass M is standing on it. At one instant, the person jumps off the round, radially away from the centre of the round (as seen from the round). The speed of the round afterwards is *

1 point

(a) 2w

(b) w

(d) 0

131. For a hollow cylinder and a solid cylinder rolling without slipping on an inclined plane, then which of these reaches earlier *

1 point

(a) solid cylinder

(b) hollow cylinder

(d) can’t say anything

132. For the adjoining diagram, the correct relation between I 1 , I 2 and I 3 is, (I – moment of inertia) *

1 point

(a) I1> I2

(b) I2> I1

(d) I3> I2

133. A point P consider at contact point of a wheel on ground which rolls on ground without slipping then value of displacement of point P when wheel completes half of rotation (If radius of wheel is 1 m) *

1 point

(a) 2 m

(b) π2 + 4 m

(d) π2 + 2 m

134. A disc is rolling, the velocity of its centre of mass is vcm. Which one will be correct? *

1 point

(a) the velocity of highest point is 2vcm and point ofcontact is zero

(b) the velocity of highest point is vcm and point of contact is vcm

(d) the velocity of highest point is 2vcm and point of contact is 2vcm

135. A circular disc is to be made by using iron and aluminium so that it acquired maximum moment of inertia about geometrical axis. It is possible with *

1 point

(a) aluminium at interior and iron surround to it

(b) iron at interior and aluminium surround to it

(d) sheet of iron is used at both external surface and aluminium sheet as internal layers

136. A disc is rotating with angular speed ω. If a child sits on it, what is conserved *

1 point

(a) linear momentum

(b) angular momentum

(d) potential energy

137. A solid sphere of radius R is placed on smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of centre of mass, which is correct? *

1 point

(a) h = R

(b) h = 2R

(d) No relation between h and R

138. A rod of length is 3 m and its mass acting per unit length is directly proportional to distance x from one of its end then its centre of gravity from that end will be at *

1 point

(a) 1.5 m

(b) 2 m

(d) 3.0 m

139. The moment of inertia of a rigid body, depends upon *

1 point

(a) distribution of mas from axis of rotation.

(b) angular velocity of the body.

(d) mass of the body.

140. A circular disc is rotating with angular velocity w. If a man standing at the edge of the disc walks towards its centre. Then , the angular velocity of the disc: *

1 point

(a) is not changed

(b) is halved

(d) increases

141. Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular velocity will be in the ratio *

1 point

(a) 2 : 1

(b) 1 : 2

(d) 1 2

142. A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle θ. The frictional forc *

1 point

(a) dissipates energy as heat

(b) decreases the rotational motion

(d) converts translational energy to rotational energy

143. A wheel has angular acceleration of 3.0 rad/s2 and an initial angular speed of 2.00 rad/s. In a time of 2 seconds it has rotated through an angle (in radian) of *

1 point

(a) 10

(b) 12

(d) 6

144. A particle of mass m moves in the XY-plane with a velocity v along the straight line AB. If the angular momentum of the particle with respect to origin O is LA when it is at A and LB when it is at B, then *

1 point

(a) LA = LB

(b) the relationship between LA and LB depends upon the slope of the line AB

(d) LA > LB

145. The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axes is *

1 point

(a) 2 1:

(b) 2 3 :

(d) 1 2

146. A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad/s. The radius of the cylinder is 0.25 m. The kinetic energy associated with the rotation of the cylinder is *

1 point

(a) 3,025 J

(b) 3,125 J

(d) 3,250 J

147. The instantaneous angular position of a point on a rotating wheel is given by the equation θ(t) = 2t 3 – 6t 2 The torque on the wheel becomes zero at *

1 point

(a) t = 1 second

(b) t = 0.5 second

(d) t = 2 seconds

148. A small mass attached to a string rotates on a frictionless table top as shown. If the tension in the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2, the kinetic energy of the mass will *

1 point

(a) decrease by a factor of 2

(b) remain constant

(d) increase by a factor of 4

149. When a mass is rotating in a plane about a fixed point, its angular momentum is directed along *

1 point

(a) a line perpendicular to the plane of rotation

(b) the line making an angle of 45 ° to the plane ofrotation

(d) the tangent to the orbit

150. The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through *

1 point

(a) B

(b) C

(d) A

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