A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top of an incline and released. The friction coefficients between the objects and the incline are same and not sufficient to allow pure rolling. The smallest kinetic energy at the bottom of the incline will be achieved by

Options

A. the work done against the frictional force is Fl.
B. the heat produced is F l.
C. W = mgh - F l
D. W gt (mgh - F l)

Answer

A, D

Explanation

In rolling with slipping, the force of friction produces a torque which gives an angular acceleration to the body. Hence, part of the work done against friction is converted to rotational kinetic energy. Only the remaining part of the work done against friction is converted to heat.