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 centre and perpendicular to one of its faces is:-
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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 cube about an axis passing through its centre and perpendicular to one of its faces is:-

G1 Physics · Accepted Answer

The largest cube has body diagonal 2R, so side a=2R/√3. With uniform density, cube mass m=2M/(√3π). For an axis through the cube centre perpendicular to a face, I=ma²/6=4MR²/(9√3π). Hence option A.