A solid sphere of radius R has its outer half removed, so that its radius becomes R 2 . Then its moment of inertia about the diameter is

Question

A solid sphere of radius R has its outer half removed, so that its radius becomes R 2 . Then its moment of inertia about the diameter is, becomes 1 2 of its intial volume, is unchanged, becomes 1 16 of initial volume., becomes 1 32 of initial volume.

MARKS App · Accepted Answer

Moment of inertia of a solid sphere is given by, I = 2 5 M R 2 = 2 5 ρ 4 3 π R 3 R 2 = 8 15 ρ π R 5 . Therefore, for constant density, the moment of inertia I ∝ R 5 . ⇒ I 1 I 2 = R 1 R 2 5 ⇒ I 2 = 1 2 5 I 1 ⇒ I 2 = 1 32 I 1

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