The radius of gyration K of a hollow sphere of mass M and radius R about an axis XY is equal to R as shown in figure. The distance of that axis from the center of the sphere is h. The value of h is

Step-by-step solution

The moment of inertia of a hollow sphere about an axis passing through its center is given by: I_ CM = 2 3 MR^2 Using the parallel axis theorem, the moment of inertia about the axis XY at a distance h from the center is: I_ XY = I_ CM + Mh^2 I_ XY = 2 3 MR^2 + Mh^2 The radius of gyration K about the axis XY is given as R . Therefore, the moment of inertia can also be written as: I_ XY = MK^2 = MR^2 Equating the two expressions for I_ XY : MR^2 = 2 3 MR^2 + Mh^2 h^2 = R^2 - 2 3 R^2 h^2 = 1 3 R^2 h = R 3 Answer: R 3