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MHT CET 2023 (13 May, Shift 2) · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from MHT CET 2023 (13 May, Shift 2)

Q93MHT CET 2023 · 13 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 $A, B, C, D.\ I_A, I_B, I_C, I_D$ are the moment of inertia of these spheres respectively about an axis passing through centre and perpendicular to the plane, then

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Answer: (c)

Each is the system MI about an axis through that centre; the $\frac{8}{5}MR^2$ part is common.
End axes (A, D): $M(4+16+36)R^2 = 56MR^2$ ; inner axes (B, C): $M(4+4+16)R^2 = 24MR^2$ .
So the answer is (c) $I_A = I_D > I_B = I_C$ .

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