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 figure.
Which of the following statement is correct?

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Both the stones reach the bottom at the same time but not with the same speed

Both the stones reach the bottom with the same speed and stone II reaches the bottom earlier than stone I

Both the stones reach the bottom at different times and with different speeds

Both the stones reach the bottom with the same speed and stone I reaches the bottom earlier than stone II

answer is C.

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Detailed Solution

As both surfaces I and II are frictionless and two stones slide from the same height, therefore, both the stones reach the bottom with same speed $(\frac{1}{2} {mv}^{2} = mgh) .$ As acceleration down the plane of stone II is larger $(a_{2} = {gsinθ}_{2} greater than a_{1} = {gsinθ}_{1})$ therefore, stone II reaches the bottom earlier than stone I.