Find the acceleration blocks in fig. The pulley and the string are massless.

Explanation

Let A be the acceleration of block M and pulley, and a be the acceleration of `m`.
Let x, X be the coordinates of m and pulley as shown.
Length of string passing over the pulley is
`L=X+(X-x)implies L=2X-x`
Differentiating twice with respect to time.
`0=2A-aimplies a=2A` ...(i)
From force diagrams of m and M, we have
`T=ma` ...(ii)
and `F-2T=MA` ...(iii)
Comparing (i), (ii) and (iii), we get `A=(F)/(M+4m)` and `a=(2F)/((M+4m))`