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 $(M+\frac{m}{2})gh$

Let us split this into parts.

FIrst bucket. Mgh

Next rope. Initially it is of length, say $h$. COM is at depth $h/2$

Net work done in pulling the rope to ground level = change in height of COM x mass of object.

$W_{rope}=mg\left(h/2\right)$

$Totalworkdone=MGH+mgh/2=(M+m/2)gh$