In the figure it is shown that the velocity of lift is `2 m s^(-1)` while string is winding on the motor shaft with velocity `2 m s^(-1)` and shaft `A` is moving downward with velocity `2 m s^(-1)` with respect to lift , then find out the velocity of block `B`

Options

A. `2 m s^(-1)uarr`
B. `2 m s^(-1)darr`
C. `4 m s^(-1)uarr`
D. None of these

Answer

D

Explanation

`nu_(AL) = nu_(A) - nu_(L)`
`:. nu_(A) = nu_(AL) + nu_(L)`
`= (-2) + 2 = 0`
Let `z =` length of string at same instant. Then

`- (dz)/(dt) = 2 m//s`
Now `y = x - (z - x) = 2x - z`
`:. (dy)/(dt) = 2 (dx)/(dt) + (-(dz)/(dt))`
`= 2 (2 m//s) + 2 m//s`
`= 6 m//s = nu_(B)`