In the figure block moves downwards with velocity `v_(1)`, the wedge rightwards with velocity `v_(2)`. The correct relation between `v_(1)` and `v_(2)` is

Options

A. `v_(2) = v_(1)`
B. `v_(2) = v_(1) sin theta`
C. `2v_(2) sin theta = v_(1)`
D. `v_(2) (1 + sin theta) = v_(1)`

Answer

D

Explanation

`z = sqrt(x^(2) + c^(2))`

Now `w + y + z = l`
or `w + y + sqrt(x^(2) + c^(2)) = l`
`:. (dw)/(dt) + (dy)/(dt) + (x)/(sqrt(x^(2) + c^(2))) . (dx)/(dt) = 0`
or `((- dw)/(dt)) + (x)/(2) ((dx)/(dt)) = (dy)/(dt)` ...(i)
`(- dw)/(dt) = - (dx)/(dt) = v_(2)`
`(dy)/(dt) = v_(1)`
`(x)/(z) = sin theta`
Substitutingthese value in Eq. (i) we have
`v_(2) + (1 + sin theta) = v_(1)`