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

Answer

D

Explanation

` F_B = V _ (rho g ) = (3m ) /(2 rho ) rho g = 1.5 mg , a_("inside") = (m_A g + F_B - 3 mg )/( m _ A + 3 m ) , a_("outside") = (3m g - m_A g ) /( m_A + 3 m ) `
As ` a _ ("inside") = a _ ("outside") rArr m _ A g + 1.5 m g - 3m g = 3 m g - m_A g rArr m _ A = (9)/(4) m `