A sphere of radius R is cut from a larger solid sphere of radius 2 R 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 2 R 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: NEET 2025

TestHub · Accepted Answer

​ I 1 ​ = 5 2 ​ M ( 2 R ) 2 I 2 ​ = 5 2 ​ mr 2 + md 2 = 5 2 ​ ( 8 M ​ ) R 2 + 8 M ​ ( R ) 2 = 40 7 MR 2 ​ I = I 1 ​ − I 2 ​ = 5 8 MR 2 ​ − 40 7 MR 2 ​ = 40 57 ​ MR 2 ​ I 1 ​ I 2 ​ ​ = 57 7 ​

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