If a solid sphere of mass 5 kg and a disc of mass 4 kg have the same radius, then 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 x 7 . The value of x is ______.

Step-by-step solution

Moment of inertia of the solid sphere about any diameter is given by, 2 m 1 R 2 5 . Using parallel axis theorem, we get I solid sphere  = 2 5 m 1 R 2 + m 1 R 2 = 7 5 m 1 R 2 = 7 5 × 5 R 2 = 7 R 2 Moment of inertia of the disc about the diameter is given by, m 2 R 2 4 . Now using parallel axis theorem, we get I disc  = m 2 R 2 4 + m 2 R 2 = 5 4 m 2 R 2 = 5 4 × 4 R 2 = 5 R 2 Therefore, I disc  I soild sphere  = 5 7 Thus, x = 5 .