In the system shown in the figure the acceleration of 1kg mass is

Options

A. `g/4` downwards
B. `g/2` downwards
C. `g/2` upwards
D. `g/4` upwards

Answer

C

Explanation

If a is downward acceleration of 4kg block, the upward acceleration of 1kg block must be 2a.
Let T be tension in each part of string
The equation of motion of 4kg block is
`T-1g=1 times 2a`…..(i)
or `2T-2g=4a`…..(iii)
Adding (i) and (iii) , we get
`2g=8a or a=8/4`
`therefore` Acceleration of 1kg block
`=2a=g/2` upwards