Question

Figure shows a fixed hemisphere of radius R and a person pulls a small body of mass m showly by a string along the rough surface of hemisphere from ground to top of sphere. coefficient of friction is $\mu$. Then works done by man against gravity and against friction in pulling the body are respectively...

• A. $\mu mgR,mgR$
• B. $mgR,\mu mgR$
• C. $mgR,\sqrt{2}\mu mgR$
• D. $mgR,\frac{\pi \mu mgR}{2}$

Answer 1

The correct option is A $\mu mgR,mgR$

Replace this block with man

so, Work done by man against gravity $=mge$

now

$wt=\Delta KE$

$w_r+w_r^0+w_{fr}+w_g=0$

But in question we have find $w_g$ and $w_{fr}$.

So

Work done by man against $f_r$ : Here $f_r$ is tangential force, $e$

so,

$\begin{array}{c}wt=\Delta KE\\ w_r+w_r^0+w_{fr}+w_g=0\\ w=\int F.ds\\ =\int -\mu mgdx\left\{-\mu mgdx\cos \theta .\frac{dx}{\cos \theta }\right\}\\ =-\mu mgR\end{array}$

Hence,

Option $A$ is correct answer.