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)/(4)m`
B. `2m`
C. `(9)/(2)m`
D. `(9)/(4)m`

Answer

D

Explanation

Acceleration when block B is in the liquid.
`a_(1)=(m_(A)g-(m_(B)g-"upthrust"))/((m_(A)+3m))`
`=(m_(A)g-(3mg-(3m)/(2rho)pig))/((m_(A)+3m))(uarr)`
Acceleration when block B is outside of the liquid.
`a_(2)=(3mg-m_(A)g)/((m_(A)+3m))(darr)` give, `a_(1)=a_(2)`
`m_(A)g=(3)/(2)mg=3mg-m_(A)g`
`2m_(A)g=(9)/(2)mg,m_(A)=((9)/(4))m`