A solid sphere of mass M and a disc of mass M 2 have the same radius. The ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be

Step-by-step solution

Let the radius of the solid sphere and the disc be R . Mass of the solid sphere, m_ s = M Mass of the disc, m_ d = M 2 Moment of inertia of the disc about its diameter is 1 4 m_ d R^2 . Using the parallel axis theorem, the moment of inertia of the disc about a tangent in its plane is: I_ disc = 1 4 m_ d R^2 + m_ d R^2 = 5 4 m_ d R^2 Substituting m_ d = M 2 : I_ disc = 5 4 ( M 2 )R^2 = 5 8 MR^2 Moment of inertia of the solid sphere about its diameter is 2 5 m_ s R^2 . Using the parallel axis theorem, the moment of i