In the system shown in fig., `m_(A)=4m`, `m_(B)=3m`, and `m_(c)=8m`. Friction is absent everywhere. String is inextensible and light. If the system is released from rest, then

Acceleration of block C is

Options

A. `g/8`
B. `g/2`
C. `g/4`
D. g

Answer

B

Explanation

a=b+c [string constrained]
`T=m_(B)b` [Newton II law for B in horizontal direction]
`T=[m_(Delta)+m_(0)]c` [Newton's I law for A and C in horizontal direction]
`m_(A)g-T=m_(A)a` [Newton's II law for A in vertical direction]
`(m_(A)g-T)/(m_(A))=T/(m_(B))+T/(m_(A)+m_(C))`
`(4mg-T)/(4m)=T/(3m)+T/(12m)`
`rArr T=(3mg)/2rArr b=g/2`