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 i $s _______.$

Question

G1 Physics · Accepted Answer

For the solid sphere about a tangent, I(sphere) = (2/5)MR² + MR² = (7/5)MR². With M = 5 kg, I(sphere) = 7R². For the disc about a tangent in its plane, I(disc) = (1/4)MR² + MR² = (5/4)MR². With M = 4 kg, I(disc) = 5R². Therefore I(disc)/I(sphere) = 5/7, so x = 5.

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 i s _______.