A wedge of height 'h' is released from rest with a light particle `P` placed on it as shown. The wedge slides down an incline which makes an angle theta with the horizontal. All the surface are smooth, `P` will reach the surface of the incline in time:

Options

A. P strikes the inclined plane in time `t=sqrt((2h)/(g sin^(2)theta))`
B. P strikes the inclined plane in time `t = sqrt((2h)/(g))`
C. P strikes the inclined plane with a speed `v=sinthetasqrt(2hg)`
D. P strikes the inclined plane with a speed `v = cos thetasqrt(2hg)`

Answer

A, B, C

Explanation

`v =at_(1) " "......(1)`
`0=v-4(3-t_(1))" ".......(2)`
Form (1) and (2)
`t_(1) = 2 sec`
`v = 2(2) = 4 m//s`
`s_(1)=(1)/(2)xx2xx2^(2)=4m`
`s_(2)=(1)/(2)xx4xx1^(2)=2m`
s = 6 m