In the arrangement shown in fig., all pulleys are smooth and massless. When the system is released from the rest, acceleration of block 2 and 3 relative to 1 are `1 ms^(-2)` downwards and `5ms^(-2)` downwards, respectively. Acceleration of block 3 relative to 4 is zero.

Find the absoulte acceleration of block 4.

Options

A. `2 ms^(-2)` upwards
B. `1 ms^(-2)` downwards
C. `3 ms^(-2)` downwards
D. `1.5 ms^(-2)` upwards

Answer

C

Explanation

Acceleration of dirrerent objects is shown in figure. All the acceleration are w.r.t. ground
Given : `a_(3)=a_(4)` ..(i)
`a_(2)+a_(1)=1` ..(ii)
`a_(3)+a_(1)=5` ..(iii)
from fig, we can write
`-a_(5)=(a_(2)+a_(3))/(2) ..(iv)`
`a_(1)=(a_(4)+a_(5))/(2)` ..(v)
Solving the above equations, we get
`a_(1)=2 ms^(-2), a_(2) = 1ms^(-2)`,
`a_(3)=a_(4)=3 ms^(-2)`.