Q: A person pulls a bucket of water from a wall of depth h. If the mass of uniform rope is m and that of the bucket full of water is M, then work done by the person is
(a) $ \displaystyle (M + \frac{m}{2})gh $
(b) $ \displaystyle \frac{1}{2}(M + m)gh $
(c) $\displaystyle (M + )gh $
(d) $ \displaystyle ( \frac{M}{2}+ m)gh $
Ans: (a)
Sol: Center of mass of the rope is at depth h/2 .
Work done= Gain in P.E
$= m g \frac{h}{2} + Mgh $