A circular disc of radius R and thickness R 6 has moment of inertia I about an axis passing through its centre and perpendicular to its plane. It is melted and recasted into a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is :

Step-by-step solution

Moment of inertia of a disc, I= 1 2 M R^2 Disc is melted and recasted into a solid sphere. Volume of sphere = Volume of disc 4 3 R₁^3= R^2 R 6 4 3 R₁^3= R^3 6 R₁^3= R^3 8 R₁= R 2 Moment of inertia of sphere, I^ = 2 5 M R₁^2= 2 5 M ( R 2 )^2= 2 5 M R^2 4 = 1 5 ( 1 2 M R^2 )= I 5