The ratio of radius of gyration of a ring to that of a disc (both circular) of same radius and mass, about a tangential axis perpendicular to the plane is

Step-by-step solution

Radius of gyration is given by, K= I m We know moment of inertia for the ring I_ disc = 1 2 m R^2 and the disc I_ ring =m R^2 about its central axis perpendicular to its plane. Using parallel axis theorem, the moment of inertia about a tangential axis perpendicular to the plane can be easily obtained using, I^ =I+m R^2 The radius of gyration is defined as: aligned & K= I m & K_ disc = 1 2 m R^2+m R^2 m = 3 2 R & K_ ring = m R^2+m R^2 m = 2 R aligned Thus, the ratio of the radius of gyration of a ring to that of a d