Question

A solid sphere of mass $m$ is placed on a rough inclined plane as shown in the figure. The coefficient $\mu$ is insufficient to start pure rolling. The sphere slides a length $\ell$ on the incline from rest and its kinetic energy becomes K. Then, the work done by friction will be

• A. $-\mu mg\ell cos\theta$
• B. $-mg\ell sin\theta +K$
• C. $-\frac{2}{5}\mu mg\ell sin\theta +K$
• D. $Noneofthese$

Answer 1

The correct option is B $-mg\ell sin\theta +K$

Work done by friction + Work done by gravity + work done by normal force = Kinetic energy K
(Work energy theorem)
work done by normal force=0
Work done by gravity is mglsin$\theta$
Work done by friction = $-mglsin\theta +K$