Question

A curved suface is shown in figure. The portion BCD is free of friction. There are three 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.
Wioth the surface AB, ball 1 has large enough friction to cause rolling down without slipping, ball 2 has a small friction and ball 3 has a negligible friction.
(a) For which ball is total mechanical energy conserved?
(b) Which ball(s) can reach D?
(c )For ball which do not reach D, which of the balls can reach back A?

Answer 1

(a) As ball 1 rolls down `AB` without slipping, friction is large enough to cause only rotation motion. However, no energy is lost due to friction. Ball 3 has negligible friction. Therefore, total mechanical energy is conserved in case of balls 1 and 3. Small friction in case of ball 2 involves some dissipation of energy. (b) Ball 3 alone can cross over `C` (lower than `A` ) and reach `D` as it has negligible friction. Ball 1 acquires some rotational energy and ball 2 loses some energy overcoming friction. They cannot reach `D`. (c) Balls 1 and 2 turn back before reaching `C`. Ball 2 cannot reach back to `A` on account of frictional losses. Ball 1 cannot roll back to `A` because of kinetic friction.