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Question

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

A
MR2322π
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B
MR2162π
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C
4MR293π
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D
4MR233π
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Solution

The correct option is C 4MR293π

When the volume of the cube is maximum, the longest diagonal of cube will be equal to diameter of the sphere.
FG=GC=LFC=(FG)2+(GC)2=L2+L2=2L& FD=(FC)2+(CD)2=(2L)2+L2=3L3L=2RL=2R3
Since massvolume, we have
MCMS=VCVSMC=VCVS×MSMC=(2R3)343πR3×MMC=2M3π
And moment of inertia of cube about an axis passing through its center and perpendicular to one of its faces is given by
I=16ML2I=16×2M3π×(2R3)2=4MR293π

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