Question

A body is moving up on inclined plane of angle $\theta$ with an initial kinetic energy $E$. The coefficient of friction between the plane and the body is $\mu$. The work done against friction before the body comes to rest is:

• A. $\frac{E\cos \theta }{\mu \cos \theta +\sin \theta }$
• B. $2\mu E\cos \theta$
• C. $\frac{\mu E\cos \theta }{\mu \cos \theta -\sin \theta }$
• D. $\frac{\mu E\cos \theta }{\mu \cos \theta +\sin \theta }$

Answer 1

The correct option is D $\frac{\mu E\cos \theta }{\mu \cos \theta +\sin \theta }$

Work energy theorem
$\frac{1}{2}m{u}^2-\frac{1}{2}m{v}^2=W=$ F. $S$
$a=-(g\sin \theta +{\mu }_{k}g\cos \theta )$
$v^2-u^2=2as$
$s=\frac{E}{mg(sin\theta +{\mu }_{k}cos\theta )}$
$f={\mu }_{k}mgcos\theta$
W $=$ F.S.$=\frac{\mu E\cos \theta }{\mu \cos \theta +\sin \theta }$