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MHT CET 2023 (9 May, Shift 2) · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from MHT CET 2023 (9 May, Shift 2)

Q104MHT CET 2023 · 9 MAY · SHIFT 2Medium

Moment of Inertia & Radius of Gyration

A disc of radius $R$ and thickness $\frac{R}{6}$ has moment of inertia I about an axis passing through its centre and perpendicular to its plane. The disc is melted and recast into a solid sphere. The moment of inertia of a sphere about its diameter is

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Answer: (a)

Volume conserved: $\pi R^2 \cdot \frac{R}{6} = \frac{4}{3}\pi a^3 \Rightarrow a = \frac{R}{2}$ .
Disc: $I = \frac{MR^2}{2}$ ; sphere: $I_s = \frac{2}{5}M\frac{R^2}{4} = \frac{MR^2}{10}$ .
$I_s = \frac{I}{5}$
So the answer is (a) $\frac{I}{5}$ .

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