Two inclined frictionless tracks, one gradual and the other steep meet at O, from where two stones are allowed to slide down from rest, one on each track. Will the stones reach the bottom at the same time ? Will they reach there with the same speed ? Explain.

Options

A. `V=O,K=E`
B. `V=E,K=O`
C. `V lt E,K=O`
D. `V=O,K lt E.`

Answer

C

Explanation

As both surfaces I and II are frictionless and two stones slide from rest from the same height, therefore, both the stones reach the bottom with same speed `((1)/(2)m upsilon^(2)=mgh)`. As acceleration down plane II is larger `(a_(2)=g sin theta_(2)` is greater than `a_(1)=g sin theta_(1))`, therefore, stone II reaches the bottom earlier than stone I.