Question

A person pulls a bucket of water from a well 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. $(M+\frac{m}{2})gh$
• B. $\frac{1}{2}(M+m)gh$
• C. $(M+m)gh$
• D. $(\frac{M}{2}+m)gh$

Answer 1

The correct option is A $(M+\frac{m}{2})gh$

Work done by the person is the change in potential energy of the bucket and the rope.
Given, the rope has a uniform mass $m$. So the center of mass for the rope is at half of the length of the rope.
So, it will be at a distance $h/2$ from the bottom.
Work done = Change in PE of bucket+Change in PE of rope
$W=Mgh+mg\frac{h}{2}=(M+\frac{m}{2})gh$
Option A.