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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Options

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 .
C. Both the stones reach the bottom with 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

Explanation

Both the stones slide rest and from the same height and they reach the bottom with the same speed
v = `sqrt(2gh)`
Acceleration down the plame I
`a_(1) = g sin theta _(1)`
Accleration down the plane II
`a_(2) = g sin theta_(2)`
Since `theta_(2) gt theta_(1) ` therefore , `a_(2) gt a_(1)` so stone II reaches the bottom earlier than stone I .