A sphere of radius R is cut from a larger solid sphere of radius 2R as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the Y-

Question

A sphere of radius R is cut from a larger solid sphere of radius 2R as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the Y-axis is:

![Question 39 as printed in the NEET 2025 booklet](/figures/neet-2025/q39.png)

Vishal Gupta · Accepted Answer

C. The removed sphere has mass \frac{M}{8} (radius halved) and its centre is R from the Y-axis: I{small} = \frac25\cdot\frac{M}{8}R^2 + \frac{M}{8}R^2 = \frac{7}{40}MR^2. The full sphere: \frac25 M(2R)^2 = \frac{8}{5}MR^2. The rest: \frac{8}{5} - \frac{7}{40} = \frac{57}{40}MR^2. Ratio = \frac{7}{57}.

System of Particles and Rotational Motion

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