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 center and perpendicular to one of its faces is?

Answer 1

good its jee Advance question//
here is the answer.

The density of the sphere is ρ=MV=M4π3R3=3M4πR3ρ=MV=M4π3R3=3M4πR3

From this sphere a cube of maximum possible volume is cut.

Therefore 2R =3√3 a, where a  is the length of the side of the cube of maximum volume  a=2R3√a=2R3

Mass of the cube is M′=ρa3=3M4πR38R333√=2M3√πM′=ρa3=3M4πR38R333=2M3π

The moment of inertia of the cube is

M′a26=2M3√π×16×(2R23√)=8MR2183√π=4MR293√πM′a26=2M3π×16×(2R23)=8MR2183π=4MR293π