In the figure acceleration of `A` is `1m//s^(2)` upward, acceleration of `B` is `7m//s^(2)` upward acceleration of `C` is `2m//s^(2)` upward. The acceleration of `D` will be.

Options

A. `7m//s^(2)` downwards
B. `2m//s^(2)` downwards
C. `10m//s^(2)` downwards
D. `8m//s^(2)` downwards

Answer

C

Explanation

Acceleration of pulley `P`
`a_(P)=(a_(A)+a_(B))/(2)=(1+7)/(2)=4m//s^(2)` (upward)
Acceleration pulley `Q` will be `4m//s^(2) downwards`.
`a_(Q)=(a_(D))-a_(C))/(2)`
`4=(a_(D)-2)/(2) implies a_(D)=10m//s^(2)(darr)` .