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1. The moment of inertia of a thin uniform rod of length L and mass M about an axis perpendicular to the rod and passing through its center is

A. (1/12)ML² B. (1/3)ML² C. (1/2)ML² D. ML²

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2. A solid sphere and a hollow sphere of the same mass and radius are released from rest at the top of an inclined plane. Which one reaches the bottom first?

A. Solid sphere B. Hollow sphere C. Both reach simultaneously D. Depends on the angle of inclination

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3. The angular momentum of a particle moving in a circle of radius r with linear speed v is

A. mvr B. mv/r C. mr/v D. mvr²

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4. The torque τ acting on a body is related to the moment of inertia I and angular acceleration α by

A. τ = Iα B. τ = I/α C. τ = α/I D. τ = I²α

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5. A disc and a ring, both of mass M and radius R, are rolling without slipping with the same linear velocity. The ratio of their kinetic energies (disc:ring) is

A. 1:1 B. 2:1 C. 1:2 D. 3:2

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6. The rotational analogue of mass in linear motion is

A. Torque B. Moment of inertia C. Angular momentum D. Angular velocity

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7. If the net external torque acting on a system is zero, then

A. Only angular velocity is conserved B. Only angular momentum is conserved C. Both angular velocity and angular momentum are conserved D. Neither angular velocity nor angular momentum is conserved

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8. A particle of mass m moves in a circular path of radius r with uniform speed v. The centripetal force is provided by a string. The work done by the string in one complete revolution is

A. 2πmv² B. πmv² C. mv² D. Zero

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9. The radius of gyration of a body of mass M and moment of inertia I about an axis is given by

A. √(I/M) B. I/M C. M/I D. √(IM)

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10. A wheel is rotating at 20 rad/s and comes to rest in 5 seconds under uniform deceleration. The angular deceleration is

A. 4 rad/s² B. -4 rad/s² C. -5 rad/s² D. 5 rad/s²

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11. The kinetic energy of a rotating body is given by

A. (1/2)Iω² B. Iω² C. (1/2)Iω D. Iω

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12. The moment of inertia of a solid cylinder of mass M and radius R about its axis is

A. (1/2)MR² B. MR² C. (1/4)MR² D. (2/5)MR²

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13. A uniform circular disc of radius R is placed on a horizontal surface and set into rotation about a vertical axis passing through its center. If μ is the coefficient of friction between the disc and the surface, then the angular velocity of the disc will decrease

A. Linearly with time B. Exponentially with time C. Quadratically with time D. Remain constant

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14. The precession of a gyroscope is due to

A. Angular momentum B. Torque C. Centripetal force D. Coriolis force

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15. A thin circular ring of mass M and radius R is rotating about its axis with a constant angular velocity ω. Its kinetic energy is

A. (1/2)MR²ω² B. (1/2)Mω² C. (1/2)Iω² D. (1/2)MRω

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16. The angular velocity of a body changes from ω₁ to ω₂ in time t under uniform angular acceleration. The angular acceleration is

A. (ω₂ - ω₁)/t B. (ω₁ - ω₂)/t C. (ω₂ + ω₁)/t D. (ω₁ + ω₂)/t

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17. A rigid body is in pure rotational motion. All the particles of the body have

A. The same linear velocity B. The same angular velocity C. Different angular velocities D. Different angular accelerations

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18. The moment of inertia of a uniform circular disc about an axis passing through its center and perpendicular to its plane is I. Its moment of inertia about a diameter is

A. I/2 B. I/4 C. 2I D. 4I

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19. A flywheel of moment of inertia I is rotating with an angular velocity ω. If a torque τ is applied opposite to its motion, the time taken to come to rest is

A. Iω/τ B. Iτ/ω C. ω/τI D. I/ωτ

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20. The center of mass of a system of particles does not depend on

A. The masses of the particles B. The positions of the particles C. The relative distances between the particles D. The velocities of the particles