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