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 ?

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 apeed 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

K = U (Conservation of energy )
`1/2 mv^(2) = mgh`
`v = sqrt(2gh)`
h is same for both stones ,hence v is same .
For stone - 1 , For stone -2 ,
`a_(1)=g sin theta_(1) " "a_(2)= gsintheta_(2)`
`a_(1)lt a_(2) ( :. theta_(1) lt theta_(2))`
Hence ,stone II reaches earlier than stone I .