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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:

Asked in NEET 2025 · Composite and cavity bodies

• (1) 7/8
• (2) 7/(40)
• (3) 7/(57)
• (4) 7/(64)

Step-by-step solution

Why the other options are wrong

• (1) No single slip gives 7/8; the cut-out sphere has only 1/8 of the mass and sits close to the axis, so its moment of inertia cannot be almost as large as that of the rest.
• (2) This is the small sphere's moment of inertia in units of MR², 7/(40)MR², not its ratio to the rest of the sphere.
• (4) Compares the small sphere with the whole sphere, (7/40)/(8/5), forgetting to take the cut-out part away.

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