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:

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Correct answer: C. 7 57

aligned & I _1= 2 5 M (2 R )^2 \ & I _2= 2 5 mr ^2+ md ^2 \ & = 2 5 ( M 8 ) R ^2+ M 8 ( R )^2 \ & = 7 MR ^2 40 \ & I = I _1- I _2= 8 MR ^2 5 - 7 MR ^2 40 = 57 40 MR ^2 aligned I _2 I _1 = 7 57

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