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 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 botom earlier than stone II
C. Both the stones reach the bottom with the same speed and stone II reaches the botom earlier than stone I
D. Both the stones reach the bottom different times and with different speeds

Explanation

(c ) As the given tracks are frictionless hence, mechaical energy will be conserved. As both the tacks having common height, h From conservation of mechanical energy
`(1)/(2)mv^(2)=mgh` (for both tracks I and II)
Hence, speed is same for both stone. For stone I, `a_(1)`=acceleration along inclined planed `=g sin theta_(1)`
Similarly, for stone II `a_(2)=g sin theta_(2) as theta_(2) gt theta_(1) hence, a_(2) gt a_(1)`,
And both length for track II is also less hence, stone II reaches earlier than stone I.