Four identical uniform solid spheres each of same mass ' M ' and… | MHT CET 2023 (14 May, Shift 2)

Q92MHT CET 2023 · 14 MAY · SHIFT 2Medium

Moment of Inertia & Radius of Gyration

Four identical uniform solid spheres each of same mass ' $M$ ' and radius ' $R$ ' are placed touching each other as shown in figure, with centres A, B, C, D. $I_A, I_B, I_C$ and $I_D$ are the moment of inertia of these spheres respectively about an axis passing through centre and perpendicular to the plane. The difference in $I_A$ , and $I_B$ is

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Answer: (b)

Centres are $2R$ apart; each sphere's own term is $\frac{2}{5}MR^2$ , same in $I_A$ and $I_B$ .
$I_A = \frac{8}{5}MR^2 + M[(2R)^2 + (4R)^2 + (6R)^2] = \frac{8}{5}MR^2 + 56MR^2$
$I_B = \frac{8}{5}MR^2 + M[(2R)^2 + (2R)^2 + (4R)^2] = \frac{8}{5}MR^2 + 24MR^2$
$I_A - I_B = 32MR^2$ , so the answer is (b).

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Moment of Inertia & Radius of Gyration question from MHT CET 2023 (14 May, Shift 2)

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