(c, d)

In rolling without slipping, no work is done against friction. Hence, loss in gravitational potential energy of a body is equal to its total kinetic energy, i.e., linear plus rotational kinetic energies. Also, v = ω ω r.

Total kinetic energy = mv 2 + I ω ω 2 = [mv 2 + (mk 2 ) (v 2 )]

= mv 2 (1 + k 2 /r 2 ), where k = radius of gyration.

As all the bodies have the same final total kinetic energy, their final velocities will depend only on the ratio k/r. Bodies with smaller values of k/r will have greater v and hence reach the bottom earlier.