question_answer 25)

Two inclined frictionless tracks, one gradual and the other steep meet at A from where two stones are allowed to slide down from rest, one on each track (Fig. 6.53). Will the stones reach the bottom at the same time ? Will they reach there with the same speed ? Explain. Given  and h = 10 m, what are the speeds and times taken by the two stones ? Fig. 6.53  

Answer:

Let  be the acceleration of the stone 1 down the inclined track AB. Then . If the stone 1 takes time ^ to slide down the track AB, then            or              Similarly, for stone 2, we can write   For both the stones, h is same. As             Consequently, Thus, the stone 2 on the steeper plane AC reaches the bottom earlier than stone 1. As both the stones are initially at the same height h, so P.E. at A = K.E. at B or C   i.e., both the stones will reach the bottom with the same speed. Given,   . . .