In the arrangement as shown, `m_(B)=3m`, density of liquid is `rho` and density of block `B` is `2rho`. The system is released from rest so that block `B` moves up when in liquid and moves down when out of liquid with the same acceleration. Find the mass of block `A`.

Options

A. `7/4m`
B. `2m`
C. `9/2m`
D. `9/4`m

Answer

D

Explanation

Acceleration when block `B` in the liquid.
`a_(1)=(m_(A)g-(m_(B)g-"upthrust"))/((m_(A)+3m))`
`=(m_(A)g-(3mg-(3m)/(2rho)rhog))/((m_(A)+3m)) (uarr)`
Acceleration when block `B` is outside of the liquid
`a_(2)=(3mg-m_(A)g)/((m_(A)+3m))(darr)`
Given `a_(1)=a_(2)` we get
`m_(A)g-3/2mg=3mg-m_(A)g`
`implies2m_(A)g-=9/2mggtm_(A)=(9/4)m`