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From a solid sphere of mass M and radius R a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its faces is

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a

4MR233π

b

MR2322π

c

MR2162π

d

4MR293π

answer is D.

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Detailed Solution

3L=2R Moment of inertia of the cubeI=ML26 =Volume×density6×L2 =ρL3L26 =M43πR3×L56 =ML54πR3(2)=M(2R3)54πR3(2) =4MR293π
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From a solid sphere of mass M and radius R a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its faces is