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 $M$, the work done by the person is:

• A. $\left(M+\frac{m}{3}\right)gh$
• B. $\frac{1}{2}\left(M+m\right)gh$
• C. $\left(M+\frac{m}{2}\right)gh$
• D. $\left(\frac{M}{2}+m\right)gh$

Answer 1

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

Solution

REF.Image

(i) When the bucket is at bottom of the well.

Let $U_{system}=0$

(ii) When the bucket has been lifted up

$U_{system}=U_{rope}+U_{Bucket}$

$U_{rope}=mg\Delta h_{COM}$

As $\Delta h_{COM}=(h-h/2)$ so,

$U_{rope}=\frac{mgh}{2}$

$U_{Bucket}=mgh$

so, $U_{system}=mgh+\frac{mgh}{2}=gh(M+\frac{m}{2})$

Option - C is correct.