question_answer 37)

                  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 as shown in Fig.                 Which of the following statement is correct?                 (a) Both the stones reach the bottom at the same time but not with the same speed.                 (b) Both the stones reach the bottom with the same speed and stone I reaches the bottom earlier than stone II. (Fig.)                 (c) Both the stones reach the bottom wit: the same speed and stone II reaches the bottom earlier than stone I.                 (d)          Both the stones reach the bottom at different times and with different speeds                

Answer:

                  (c) \[\upsilon \,=\,\sqrt{2gh}.\] Since h is same in both the cases, so speed of both the stones at the bottom is same.                 Time taken to reach the bottom is directly proportional to the length of the track. Since length of track for stone II is less than that of for particle I, so stone II reaches earlier than stone I.