(a) Show that the rotational inertia of a solid cylinder of mass M and radius R about its central axis is equal to the rotational inertia of a thin hoop of mass M and radius R/√2 about its central axis.
(b) Show that the rotational inertia 1 of any given body of mass M about any given axis is equal to the rotational inertia of an equivalent hoop about that axis, if the hoop has the same mass M and a radius k given by k = √1/M. The radius k of the equivalent hoop is called the radius of gyration of the given body.