From a solid sphere of mass M and radius R , a cube of the 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:

Step-by-step solution

Let a be the length of edge for the cube, with maximum possible volume diagonal length = 2 R ⇒ 3 a = 2 R ⇒ a = 2 R 3 . As densities of sphere and cube are equal. Let M ' be mass of the cube, M 4 3 π R 3 = M ' a 3 ⇒ M ′ = 3 M a 3 4 π R 3 . Moment of inertia of cube about an axis passing through its center is, I = M ′ 2 a 2 12  = 3 M a 3 4 π R 3 × 2 a 2 12  = M a 5 8 π R 3 . also, a = 2 3 R ⇒ I  = M × 32   R 5 8 π × 9 3 R