A curved surface is shown in figure. The portion BCD is frictionless. There are two spherical balls of identical radii and masses. Balls are released from rest one by one from A which is at a slightly greater height than C. With the surface AB ball 1 has a small friction and ball 2 has a negligible friction. For which balls is total mechanical energy conserved?

Explanation

(a) As ball 1 is rolling down without slipping there is no dissipation of energy, hence total mechanical energy is conserved.
(b) Ball 1 acquires rotational energy, ball 2 loses energt by friction. They cannot cross at C. Ball # can cross over.
(c ) Balls 1 and 2 turn back before reaching C. Because of loss of energy, ball 2 cannot reach back to A. Ball 1 has a rotational motion in wrong sense when it reaches B. It cannot roll back to A because of kinetic friction.