Physics - NLM Question with Solution | TestHub

The force $P$ on the pulley is shared equally by the two rope segments, so a net horizontal force $P/2$ acts on the bracket and $P/2$ on the block (surfaces smooth).

Each has mass $m$: $a_1=a_2=\frac{P/2}{m}=\frac{P}{2m}$. So the acceleration of the pulley in the ground frame is $\frac{P}{2m}$.