A thin circular ring and a solid cylinder have the same mass and the same radius. The ratio of the radius of gyration of the ring about its central axis to the radius of gyration of the solid cylinder about its central axis is:

Step-by-step solution

The moment of inertia of a thin circular ring of mass M and radius R about its central axis is I_ ring = MR^2 . The radius of gyration for the ring is k_ ring = I_ ring M = MR^2 M = R . The moment of inertia of a solid cylinder of mass M and radius R about its central axis is I_ cyl = 1 2 MR^2 . The radius of gyration for the solid cylinder is k_ cyl = I_ cyl M = MR^2 2M = R 2 . The required ratio is k_ ring k_ cyl = R R/ 2 = 2 1 , which is 2 :1 . Answer: 2 :1