NEET 2025 · PhysicsPrevious Year Question
A sphere of radius R is carved out of a uniform solid sphere of radius 2R (internally tangent, so its centre is at distance R from the big centre). The ratio of the moment of inertia of the small sphere to that of the remaining part, both about the Y-axis through the big sphere's centre, is:
- A.7/57✓
- B.7/64
- C.7/8
- D.7/40
Correct Answer
(A) 7/57
Solution & Explanation
Correct Answer (A): 7/57 Solution: Let small mass m → big mass M=8m (volume (2R)³=8R³). I_small about Y = (2/5)mR² + mR² = 7/5 mR². I_big(full) about Y = (2/5)(8m)(2R)² = 64/5 mR². I_rest = 64/5 - 7/5 = 57/5 mR². Ratio = (7/5)/(57/5) = 7/57.
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