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

Options

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

Answer

C

Explanation

If a downward acceleration of 4 kg block, the upward acceleration of 1 kg block must be 2a. Let T be tension in each part of string. The equation of motion on 4 kg block is 4g-2T=4a
The equation of motion on 1 kg block is
`T-1g=1xx2a`
or `2T-2g=4a...(ii)`
or 2T-2g=4a...(iii)
Adding (i) and (iii), we get
`therefore "Acceleration of 1 kg block"=2a=(g)/(2)"upwards"`