The ratio of the radius of gyration of a uniform solid sphere about an axis tangent to its surface to the radius of gyration of the sphere about its diameter is

Step-by-step solution

For a uniform solid sphere of mass M and radius R : Moment of inertia about its diameter is I_ diameter = 2 5 MR^2 . Radius of gyration about the diameter, k_ diameter = I_ diameter M = 2 5 R . Using the parallel axis theorem, the moment of inertia about a tangent is I_ tangent = I_ diameter + MR^2 = 2 5 MR^2 + MR^2 = 7 5 MR^2 . Radius of gyration about the tangent, k_ tangent = I_ tangent M = 7 5 R . The required ratio is k_ tangent k_ diameter = 7/5 R 2/5 R = 7 2 . Answer: 7 : 2