Newton's Laws of Motion - Question on Attwood's Machine

Question

With regret I am unable to answer the following question. Any assistance rendered would be very gratefully received

Answer 1

First, consider the movement from A to B:

Newton's second law gives $$mg = (2M+m)a$$where $a$ is the acceleration from A to B. So we get $$a=\frac{mg}{2M+m}.$$ Besides, $v=at_{AB}$ and $h=\frac{1}{2}at_{AB}^2$ gives $v=\sqrt{2ah}$, where $v$ is the speed at B.

Secondly, consider the movement from B to C: $$vt=h$$ Put in $v=\sqrt{2ah}$, after some simple algebra, you can get $$g=\frac{h(2M+m)}{2mt^2}$$