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MHT CET202527 Apr 2025Evening ShiftPhysicsRotational MotionActual

A solid sphere is in purely rotational motion about its diameter. The ratio of its angular momentum and kinetic energy is 22 . Find angular velocity of the sphere. ( =22 / 7 )

Options

  1. A10 rad / s
  2. B7 rad / s
  3. C14 rad / s
  4. D21 rad / s

Correct answer

A. 10 rad / s

Step-by-step solution

Angular momentum and rotational kinetic energy relate through the moment of inertia I = 2 5 MR^2 and angular velocity as L = I and K = 1 2 I ^2 respectively. The ratio simplifies to L K = I 1 2 I ^2 = 2 . Given L K = 22 , we equate 2 = 22 . Solving for angular velocity: = 44 . Substituting = 22 7 yields = 44 7 22 = 14 rad/s. The angular velocity is therefore 14 rad/s.

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