AjneeshFlame Institute

91. The total kinetic energy of a body of mass 10 kg and radius 0.5 m moving with a velocity of 2 m/s without slipping is 32.8 joule. The radius of gyration of the body is

(a) 0.25 m (b) 0.2 m (c) 0.5 m (d) 0.4 m Ans. d (37)

88. In a playground there is a merry-go-round of mass 120 kg and radius 4 m. The radius of gyration is 3m. A child of mass 30 kg runs at a speed of 5 m/sec tangent to the rim of the merry-go-round when it is at rest and then jumps on it. Neglect friction and find the angular velocity of the merry-go-round and child

(a) 0.2 rad/sec (b) 0.1 rad/sec (c) 0.4 rad/sec (d) 0.8 rad/sec Ans. c (74)

83. A particle undergoes uniform circular motion. About which point on the plane of the circle, will the angular momentum of the particle remain conserved

(a) Centre of the circle (b) On the circumference of the circle (c) Inside the circle (d) Outside the circle Ans. a (5)

81. A rigid spherical body is spinning around an axis without any external torque. Due to change in temperature, the volume increases by 1%. Its angular speed

(a) Will increase approximately by 1% (b) Will decrease approximately by 1% (c) Will decrease approximately by 0.67% (d) Will decrease approximately by 0.33% Ans. c (7)

A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity ω. 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 angular velocity

(a) ω(M-2m) /(M+2m) (b) ωM/M+2m) (c) ωM/M+m (d) ω(M+2m)/M Ans. b (39)

78. An equilateral triangle ABC formed from a uniform wire has two small identical beads initially located at A. The triangle is set rotating about the vertical axis AO. Then the beads are released from rest simultaneously and allowed to slide down, one along AB and the other along AC as shown. Neglecting frictional effects, the quantities that are conserved as the beads slide down, are

(a) Angular velocity and total energy (kinetic and potential) (b) Total angular momentum and total energy (c) Angular velocity and moment of inertia about the axis of rotation (d) Total angular momentum and moment of inertia about …

77. A uniform heavy disc is rotating at constant angular velocity ω about a vertical axis through its centre and perpendicular to the plane of the disc. Let L be its angular momentum. A lump of plasticine is dropped vertically on the disc and sticks to it. Which will be constant

(a) w (b) w and L both (c) L only (d) Neither w nor L Ans. c (45)

76.

Two rigid bodies A and B rotate with rotational kinetic energies EA and EB respectively. The moments of inertia of A and B about the axis of rotation are IA and IB respectively. If IA = IB /4 and EA …

75. A particle of mass m moves along line PC with velocity v as shown. What is the angular momentum of the particle about O

(a) mvL (b) mvl (c) mvr (d) Zero Ans. b (3)

74. A disc is rotating with an angular speed of ω. If a child sits on it, which of the following is conserved

(a) Kinetic energy (b) Potential energy (c) Linear momentum (d) Angular momentum Ans. d (11)

73. The motion of planets in the solar system is an example of the conservation of

(a) Mass (b) Linear momentum (c) Angular momentum (d) Energy Ans. c (7)

72. A thin rod of length L and mass M is bent at the middle point O at an angle of 60 degree as shown in figure. The moment of inertia of the rod about an axis passing through O and perpendicular to the plane of the rod will be

(a) ML2/6 (b) ML2/12 (c) ML2/24 (d) ML2/3 Ans. b (29)

71. The moment of inertia I of a solid sphere having fixed volume depends upon its volume V as

(a) I ∝ V (b) I ∝ V2/3 (c) I ∝ V5/3 (d) I ∝ V3/2 Ans. c (10)

70. Four solids are shown in cross section. The sections have equal heights and equal maximum widths. They have the same mass. The one which has the largest rotational inertia about a perpendicular through the centre of mass is

Ans. a (126)

A thin wire of length L and uniform linear mass density ρ is bent into a circular loop with centre at O as shown. The moment of inertia of the loop about the axis XX’ is

(a) ρL3/8π2 (b) ρL3/16π2 (c) 5ρL3/16π2 (d) 3ρL3/8π2 Ans. d (8)

63. Two discs of same thickness but of different radii are made of two different materials such that their masses are same. The densities of the materials are in the ratio 1 : 3. The moments of inertia of these discs about the respective axes passing through their centres and perpendicular to their planes will be in the ratio

(a) 1 : 3 (b) 3 : 1 (c) 1 : 9 (d) 9 : 1 Ans. b (45)

68. A thin wire of length l and mass M is bent in the form of a semi-circle. What is its moment of inertia about an axis passing through the ends of the wire

(a) ML2/2 (b) ML2/π2 (c) 2ML2/ π2 (d) 2ML2/2π2 Ans. d (3)

66. Two point masses of 0.3 kg and 0.7 kg are fixed at the ends of a rod of length 1.4 m and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum is located at a distance of

(a) 0.4 m from mass of 0.3 kg (b) 0.98 from mass of 0.3 kg (c) 0.70 m from mass of 0.7 kg (d) 0.98 m from mass of 0.7 kg Ans. b (7)

65. If solid sphere and solid cylinder of same radius and density rotate about their own axis, the moment of inertia will be greater for (L = R)

(a) Solid sphere (b) Solid cylinder (c) Both (d) Equal both Ans. a (45)

62. One quarter sector is cut from a uniform circular disc of radius R. This sector has mass M. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation is

(a) 1/2 MR2 (b) 1/4 MR2 (c) 1/8 MR2 (d) √2 MR2 Ans. a (6)

61. From a uniform wire, two circular loops are made (i) P of radius r and (ii) Q of radius nr. If the moment of inertia of Q about an axis passing through its centre and perpendicular to its plane is 8 times that of P about a similar axis, the value of n is (diameter of the wire is very much smaller than r or nr)

(a) 8 (b) 6 (c) 4 (d) 2 Ans. d (6)

60. We have two spheres, one of which is hollow and the other solid. They have identical masses and moment of inertia about their respective diameters. The ratio of their radius is given by

(a) 5:7 (b) 3:5 (c) √3:√5 (d) √3:√7 Ans. c (8)

The adjoining figure shows a disc of mass M and radius R lying in the X-Y plane with its centre on X-axis at a distance α from the origin. Then the moment of inertia of the disc about the X-axis is

(a) M(R2/2) (b) M(R2/4) (c) M(R2/4+a2) (d) M(R2/2+a2) Ans.b (39)

What is the moment of inertia of a square sheet of side l and mass per unit area μ about an axis passing through the centre and perpendicular to its plane

(a) μl2/12 (b) μl2/6 (c) μl4/12 (d) μl4/6 Ans. d (7)

According to the theorem of parallel axes I=Ig+Md2 , the graph between l and d will be

Ans. c (5)

56. On account of melting of ice at the north pole the moment of inertia of spinning earth

(a) Increases (b) Decreases (c) Remains unchanged (d) Depends on the time Ans. a (13)

55. Three particles are situated on a light and rigid rod along Y axis as shown in the figure. If the system is rotating with an angular velocity 2 rad/s of about X axis, then the total kinetic energy of the system is

(a) 92 J (b) 184 J (c) 276 J (d) 46 J Ans. b (53)

54. Moment of inertia of a sphere of mass M and radius R is I. Keeping constant if a graph is plotted between I and R, then its form would be

Ans. d (21)

Two loops P and Q are made from a uniform wire. The radii of P and Q are r1 and r2 respectively, and their moments of inertia are l1 and l2 respectively. If l2/l1=4 then r2/r1 equals

(a) 42/3 (b) 41/3 (c) 4-2/3 (d) 4-1/3 Ans. b (18)

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

(a) Ml2/3 (b) Ml2/4 (c) 2Ml2/3 (d) 4Ml2/3 Ans. d (8)

The moment of inertia of a sphere (mass M and radius R) about it’s diameter is I. Four such spheres are arranged as shown in the figure. The moment of inertia of the system about axis xx’ will be

(a) 3I (b) 5 I (c) 7 I (d) 9 I Ans. d (16)

50. In a rectangle ABCD (BC=2AB) . The moment of inertia along which axis will be minimum

(a) BC (b) BD (c) HF (d) EG Ans. d (36)

49. Three point masses m1, m2, m3 are located at the vertices of an equilateral triangle of length ‘a’ . The moment of inertia of the system about an axis along the altitude of the triangle passing through m1 is

(a) (m2+m3)a4/4 (b) (m 1+m2+m 3)a2 (c) (m1+m2)a2/2 (d) (m2+m3)a2 Ans. a (47)

47. Four particles each of mass m are placed at the corners of a square of side length l. The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is

(a) l/ √2 (b) l/2 (c) l (d) (√2)l Ans. a (31)

48. The moment of inertia of a rod (length l, mass m) about an axis perpendicular to the length of the rod and passing through a point equidistant from its mid point and one end is

(a) ml2/12 (b) 7/48 ml2 (c) 13 ml2 (d) 19/48ml2 Ans. b (5)

43. A circular disc is to be made by using iron and aluminium, so that it acquires maximum moment of inertia about its geometrical axis. It is possible with

(a) Iron and aluminium layers in alternate order (b) Aluminium at interior and iron surrounding it (c) Iron at interior and aluminium surrounding it (d) Either (a) or (c) Ans. b (3)