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AP EAMCET202023 Sep 2020Morning ShiftPhysicsRotational MotionActual

If the radius of a sphere is doubled by keeping its mass constant, compare the moment of inertia of the old sphere with that of the new sphere, about any diameter.

Options

  1. AI 1 : I 2 = 1 : 4
  2. BI 1 : I 2 = 1 : 2
  3. CI 1 : I 2 = 4 : 1
  4. DI 1 : I 2 = 2 : 1

Correct answer

A. I 1 : I 2 = 1 : 4

Step-by-step solution

Moment of inertia of the sphere I = 2 m r 2 5 Moment of inertia of the old sphere I old = 2 m r 2 5 Moment of inertia of the old sphere I new = 2 m 2 r 2 5 Ratio of moment of inertia of the old sphere to new sphere I old I new = 2 m r 2 5 2 m 2 r 2 5 = 1 4

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