b) 2/3 MR 2 c) 3/4MR 2 d) 2/5MR 2

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1 Rotational Motion 1) The diameter of a flywheel increases by 1%. What will be percentage increase in moment of inertia about axis of symmetry a) 2% b) 4% c) 1% d) 0.5% 2) Two rings of the same radius and mass are placed such that their centers are at common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centers and perpendicular to the plane of the ring is ( mass of ring =m, radius =r) a) 1/2mr 2 b) mr 2 c) 3/4 mr 2 d) 2 mr 2 3) A body of mass M and radius R is rolling horizontally without slipping with speed V. if then rolls up hill to a maximum height h. If h=5v2/6g, what is the moment of inertia of the body? a) 1/2MR 2

2 b) 2/3 MR 2 c) 3/4MR 2 d) 2/5MR 2 4) A wire of mass m and length l is bent in the form of a circular ring. The moment of inertia of the ring about its axis is a) Ml 2 b) Ml 2 /2ᴨ 2 c) Ml 2 /4ᴨ 2 d) Ml 2 /6ᴨ 2 5) The moment of inertia of a uniform disc about an axis passing through its centers and perpendicular to its plane is 1kg/m 2. It is rotating with an angular velocity 100 rad/sec. another identical disc is gently placed on it so that their centers coincide. Now, these two discs together continue to rotate about the same axis. Then loss in kinetic energy in kilojoules is a) 2.5 b) 3 c) 3.5 d) 4

3 6) The moment of inertia of a uniform rod about a perpendicular axis passing through one end is I 1. The same rod is bent into a ring and its moment of inertia about a diameter is I 2 then I 1 / I 2 is a) ᴨ 2 /3 b) 2ᴨ 2 /3 c) 4ᴨ 2 /3 d) 8ᴨ 2 /3 7) A wire of mass m and length l is bent in the form of a circular ring, the moment of inertia of the ring about its axis is a) (1/8ᴨ 2 )ml 2 b) (1/2ᴨ 2 )ml 2 c) (1/4ᴨ 2 )ml 2 d) ml 2 8) A uniform disc of mass M and radius R is mounted on an axis supported by frictionless bearings. A light cord is wrapped around the rim of the disc and steady downward pull T is exerted on the cord. The angular acceleration of the disc is

4 a) T/MR b) 3T/2MR c) 2T/MR d) T/2MR 9) 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 the moment of inertia of the system doubles. The kinetic energy of the system is a) 2K b) K/2 c) K/4 d) 4K 10) 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 a) 2:1 b) 2: 3

5 c) 3: 2 d) 1: 2 11) Consider a system of two particles having masses m 1 and m 2. If the particle of mass m 1 is pushed towards the mass centre of particles through a distance d, by what distance would the particles of mass m 2 move so as to keep the mass centers of particles at the original position? a) d b) (m 2 /m 1 )d c) [m 1 /(m 1 +m 2 )]d d) (m 2 /m 1 )d 12) The moment of inertia of a body about a given axis is 1.2 kgm 2. Initially, the body is at rest. In order to produce a rotational kinetic energy of 1500 J, an angular acceleration of 25 rad/s 2 must be applied about that axis for a duration of a) 4 s b) 8 s c) 2 s

6 d) 10 s 13) Moment of inertia of a rod of mass M, length L about an axis perpendicular to it through a point L/4 from one end a) ML 2 /12 b) (7/48) ML 2 c) (3/24) ML 2 d) (5/36) ML 2 14) One solid sphere A and another hollow sphere B are of same mass and same outer radii, their moment of inertia about their diameter are respectively I A and I B such that a) I A = I B b) I A > I B c) I A < I B d) I A /I B = d A /d B

7 15) A wheel whose moment of inertia is 12 kgm 2 has an initial angular velocity of 40 rad/s. A constant torque of 20 Nm acts in the wheel. The time in which the wheel is accelerated to 100 rad/s is a) 72 sec b) 16 sec c) 8 sec d) 36 sec 16) Three point masses m 1,m 2 and m 3 are located at the vertices of an equilateral triangle of side a what is the M.I. of the system about an axis along the altitude of the triangle passing through m 1 a) (m 1 +m 2 )a 2 /4 b) (m 2 +m 3 )a 2 /4 c) (m 1 +m 3 )a 2 /4 d) (m 1 +m 2 +m 3 )a 2 /4 17) A circular ring of mass M and radius R is rotating about its axis at an angular frequency ω. Two blocks each of mass m are gently placed on the opposite ends of a diameter of the ring. The angular frequency of the ring becomes ώ the ratio ώ/ω is a) M/(M+2m) b) 2M/(M+2m) c) 2m/M

8 d) M/2m 18) A particle perform U.C.M. with an angular momentum L. if the angular frequency of the particles is doubled and K.E. is halved, its angular momentum becomes a) 4L b) 2L c) L/2 d) L/4 19) Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertia I and 2I resp. about the common axis. Disc A is imparted an initial angular velocity 2ω using the centers P.E. of a spring compressed by a distance X 1. Disc B is imparted an angular velocity ω by a spring having the same spring constant and compressed by distance X 2. Both the discs rotate in the clockwise direction. The ratio X 1 /X 2 is a) 2 b) 1/2 c) 2 d) 1/ 2

9 20) A ring and a disc of different masses are rotating with the same K.E. If a rotating torque is applied to the ring, the ring stops after completing n rotations. If the same retarding torque is applied to the disc, how many rotations would it complete before coming to rest? a) 2n b) 4n c) n/2 d) n 21) A light rod of length L has two masses m 1 and m 2 attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod sand passing through the center of mass is a) (m 1 + m 2 ) L 2 b) ( m 1 m 2 )L 2 c) (m 1 m 2 / m 1 + m 2 ) L 2 d) (m 1 + m 2 / m 1 m 2 ) L 2 22) A child standing with folded hands at the center of a platform rotating about its central axis. The K.E. of the system is K. The child now stretches his arms so that the M.I. of the system doubles. What is new kinetic energy of the system? a) K

10 b) 2K c) K/2 d) K/4 23) A solid cylinder of mass M and radius R rolls down on inclined plane of height h. what is its rotational K.E. when it reaches the foot of the plane? a) Mgh/2 b) Mgh/3 c) Mgh/4 d) 2/3 *Mgh 24) Initial angular velocity of a circular disc of mass M is ω 1. Then two small spheres of mass m are attached gently to two diametrically opposite points on the edge of the disc. Then final angular velocity of the disc is a) (M+m/M) ω 1 b) (M+4m/M) ω 1 c) (M/M+4m) ω 1 d) (M/M+2m) ω 1

11 25) 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 the M.I. of the system doubles. The kinetic energy of the system now is a) 2K b) K/2 c) K/4 d) 4K