The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axes is

Step-by-step solution

Key Idea : The square root of the ratio of the moment of inertia of a rigid body and its mass is called radius of gyration. As in key idea, radius of gyration is given by K= I M For given problem K_ disc K_ ring = I_ disc I_ ring But I_ disc (about its axis) = 1 2 M R^2 and I_ ring (about its axis) =M R^2 where R is the radius of both bodies. Therefore, Eq. (i) becomes K_ disc K_ ring = 1 2 M R^2 M R^2 =1: 2