Question

Work done in moving a body up on an inclined rough plane ($\mu$) of length $S$ will be

• A. $mg(sin\theta +{\mu }_{k}cos\theta )S$
• B. $mg({\mu }_{k}sin\theta +cos\theta )S$
• C. $mg({\mu }_{k}sin\theta -cos\theta )S$
• D. $mg(sin\theta -{\mu }_{k}cos\theta )S$

Answer 1

The correct option is A $mg(sin\theta +{\mu }_{k}cos\theta )S$

Equating the forces along the incline plane and normal to inclined plane,
where $mgsin\theta$ is the parallel component of weight and $mgcos\theta$ is the normal component
$N=mgcos\theta$
$f={\mu }_{k}mgcos\theta$
Also,
$F=mgsin\theta +{\mu }_{k}mgcos\theta$
$\therefore W=(mgsin\theta +{\mu }_{k}mgcos\theta )\times S$