Physics - NLM Question with Solution | TestHub

Let $a_B$ be the acceleration of the block (and the rope) relative to the ground. Let $a_M$ be the acceleration of the man relative to the ground.

The acceleration of the man relative to the rope is $a_r$. Since the man climbs up and the rope moves down (with acceleration $a_B$), $a_M=a_r-a_B$. For the block: $T=M{a}_B$. For the man: $T-mg=m{a}_M=m(a_r-a_B)$. Substituting $T$: $M{a}_B-mg=m{a}_r-m{a}_B$. Rearranging, $(M+m)a_B=m(g+a_r)$. Thus, $a_B=\frac{m(g+a_r)}{M+m}$.