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MHT CET 2023 (10 May, Shift 2) · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from MHT CET 2023 (10 May, Shift 2)

Q94MHT CET 2023 · 10 MAY · SHIFT 2Medium

Moment of Inertia & Radius of Gyration

Two spheres each of mass ' $M$ ' and radius $\frac{R}{2}$ are connected at the ends of massless rod of length ' $2R$ '. What will be the moment of inertia of the system about an axis passing through centre of one of the spheres and perpendicular to the rod?

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Answer: (d)

Each sphere: $\frac{2}{5}M\left(\frac{R}{2}\right)^2 = \frac{MR^2}{10}$ ; centres $2R$ apart.
$I = \frac{MR^2}{10} + \frac{MR^2}{10} + M(2R)^2$
$I = \frac{1}{5}MR^2 + 4MR^2 = \frac{21}{5}MR^2$ , so the answer is (d).

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