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MHT CET202619 April 2026Morning ShiftPhysicsRotational MotionActual

The radius of gyration of a solid sphere of radius 'R' and mass 'M' about its diameter is K_d and that about a tangent of a solid sphere is K_t . The ratio of K_d to K_t is

Options

  1. A( 7 5 )^ 1/2
  2. B( 7 2 )^ 1/2
  3. C( 2 7 )^ 1/2
  4. D( 2 5 )^ 1/2

Correct answer

C. ( 2 7 )^ 1/2

Step-by-step solution

The moment of inertia of a solid sphere about its diameter is I_d = 2 5 MR^2 . The radius of gyration about the diameter is K_d = 2 5 R . Using the parallel axis theorem, the moment of inertia of the solid sphere about a tangent is I_t = I_d + MR^2 = 2 5 MR^2 + MR^2 = 7 5 MR^2 . The radius of gyration about the tangent is K_t = 7 5 R . The ratio of K_d to K_t is K_d K_t = 2 5 R 7 5 R = ( 2 7 )^ 1/2 . Answer: ( 2 7 )^ 1/2

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