Find the acceleration of each block in the situation shown in the figure. All the surface are smooth and the pulleys and sttings are light.

Explanation

In this problem, two blocks are moving with different acceleration because they travel different distances in same time. If blocks travel different distances in same time. Their accelerations are proportional to distance travelled.
Considwer the motion of pulley `B`, if it goes down by a distance `x_(0)`, the block of mass `2m` will also move by `x_(0)` but the block of mass `m` will move by `2x_(0)`. If an acceleration of `2m` is `a`, the acceleration of `m` will be `2a`

`2m:darr:2mg-2T=2ma` (i)
`mrarr:T=mxx2a` (ii)
From (i) and (ii)
`2mg-4ma=2marArr6ma=2mgrArra=(g)/(3)`
Acceleration of `2m:(g)/(3)`
`m:(2g)/(3)`