A small, light pulley is attached with a block C of mass 4 kg as shown in fig. Block B of mass 1.5 kg is placed on the top horizontal surface of C. Another block A of mass 2 kg is hanging from a string, attached with B and passing over the pulley. Taking `g=10ms^(-2)` and neglecting friction, calculate the acceleration of each block when the system is released from rest.

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`