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

A. 1/2 MR² B. 1/4 MR² C. MR² D. 1/3 MR²

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2. A flywheel rotating with angular velocity ω has rotational kinetic energy E. If its angular velocity is doubled, the new rotational kinetic energy will be

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

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3. A thin ring of mass M and radius R is rotating about an axis passing through its diameter. The moment of inertia of the ring is

A. MR² B. 1/2 MR² C. 1/4 MR² D. 1/3 MR²

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4. A particle is rotating in a circle of radius R with a constant angular speed ω. The centripetal force is proportional to

A. ω B. ω² C. 1/ω D. 1/ω²

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5. A disc rotates about its central axis. The ratio of its angular velocity to its frequency is

A. 2π B. π C. 1/2π D. 1

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6. A uniform rod of length L is pivoted at its center and rotates in a horizontal plane. The moment of inertia of the rod is

A. 1/3 ML² B. 1/4 ML² C. 1/12 ML² D. 1/2 ML²

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7. The angular acceleration of a rotating body is constant. The relation between angular displacement θ, angular velocity ω, and angular acceleration α is

A. θ = ωt + 1/2 αt² B. θ = ωt² + 1/2 αt C. θ = 1/2 ωt² + αt D. θ = ω² + αt

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8. A hollow sphere of radius R and mass M is rotating about its diameter. Its moment of inertia is

A. 2/5 MR² B. 2/3 MR² C. 2MR² D. 5/3 MR²

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9. A solid sphere rolls without slipping on an inclined plane. The minimum coefficient of friction required is

A. 2/5 B. 1/2 C. 1/7 D. 1/3

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10. A disc rotating with an angular velocity ω is subjected to a constant torque. Its angular displacement in time t is

A. ωt + 1/2 αt² B. ωt² + 1/2 αt C. 1/2 ωt² + αt D. ω² + αt

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11. The ratio of angular speeds of two discs is 2:3. If their moments of inertia are in the ratio 3:2, the ratio of their angular momenta is

A. 2:3 B. 1:1 C. 3:2 D. 4:9

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12. A rigid body is rotating about a fixed axis. If the angular acceleration is zero, the torque acting on the body is

A. Maximum B. Minimum C. Zero D. Constant

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13. A particle moves in a circular path with constant speed. Its angular momentum remains

A. Constant in magnitude and direction B. Constant in magnitude but changes in direction C. Changes in magnitude and direction D. None of these

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14. The angular velocity of Earth about its own axis is

A. 1 rad/s B. 2π rad/s C. π/12 rad/s D. 2π/24 rad/s

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15. A wheel of radius R rolls on a horizontal surface with a constant velocity v. The ratio of translational to rotational kinetic energy is

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

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

A. ML²/3 B. ML²/12 C. ML²/2 D. ML²/6

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17. A torque is applied to a rotating object. The angular acceleration produced is inversely proportional to

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

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18. A disc is subjected to a constant torque. If its moment of inertia is doubled, the angular acceleration will become

A. Half B. Double C. Four times D. Unchanged

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19. The angular velocity of a particle increases linearly with time. The angular acceleration is

A. Constant B. Zero C. Variable D. None of these

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20. A solid cylinder and a hollow cylinder of the same mass and radius roll down an inclined plane. Which will reach the bottom first?

A. Solid cylinder B. Hollow cylinder C. Both simultaneously D. Depends on the incline angle