Q 11-04-027JEE MainEAMCET 2013 (Engineering)Hard
The upper half of an inclined plane of inclination $\theta$ is perfectly smooth while the lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom. The coefficient of friction between the block and the lower half of the plane is given by
Answer: (A) $\mu = 2\tan\theta$
Let the plane have length $2L$. The block starts and ends at rest, so the work done by gravity over the whole length equals the work done against friction over the lower half:
$$mg\sin\theta\,(2L) = \mu mg\cos\theta\,(L) \;\Rightarrow\; \mu = 2\tan\theta$$
Solution by Sreeraj P, M.Sc Physics