The ratio of radii of gyration of a circular ring and a circular disc, of the same mass and radius about an axis passing through their centres and perpendicular to their planes are:

Step-by-step solution

Let M and R be the mass and radius of ring and disc then M.I. of ring about an axis passing through its centre and perpendicular to its plane is I_ ring =M R^2 And M.I. of disc about an axis passing through centre is aligned & I_ disc = M R^2 2 & i.e. aligned I & =M K^2 where K= radius of & gyration I_ ring & =M K_ ring ^2 & =M R^2 I_ fring & =R I_ disc & =M K_ disc ^2 & = M K^2 2 K_ disc & = R 2 aligned aligned aligned K _ ring K _ desc & = R R 2 = 2 1 & = 2 : 1 aligned