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 length of edge for cube with maximum possible volume diagonal length = 2R ⇒ 3 a = 2 R ⇒ a = 2 R 3 As densities of sphere and cube are equal. Let M' be mass of 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 centre 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 3 = 4 M R 2 9 3 π