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A curved surface as shown in the figure. The portion BCD is free of friction. There are three spherical balls of identical radii and masses. Balls are released from one by one from A which is at a slightly greater height than C. with the surface AB, ball 1 has large enough friction to cause rolling down without slipping; ball 2 has small friction and ball 3 has negligible friction.

a) for which balls is total mechanical energy conserved?

b) which ball can reach D?

c) for balls which do not reach D, which of the balls can reach back A?

Answers (1)

(a) For which ball is total mechanical energy conserved?

For balls 1 and 3, the total mechanical energy is conserved. In the case of ball 1, it rolls down without slipping and hence no force of friction acts against its motion and no energy is dissipated. In the case of ball 3, it has negligible friction, and hence, there is no loss of energy which leads to the conservation of mechanical energy.

(b) Which ball (s) can reach D?

Ball 1 slips due to its acquired rotational energy on the frictionless surface. Ball 2 loses its energy due to friction. Hence, it does not reach C.

(c) For balls which do not reach D, which of the balls can reach back A?

As we saw, balls 1 and 2 do not reach C, and hence they also don’t reach D.

Ball 3 has negligible friction and hence can reach D. for balls 1 and 2, no of them can reach back at A.

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