Question

A small block starts slipping down from a point $B$ on an inclined plane $AB$, which is making an angle $\theta$ with the horizontal section $BC$ is smooth and the remaining section $CA$ is rough with a coefficient of friction $\mu$. It is found that the block comes to rest as it reaches the bottom (point A) of the inclined plane. If $BC=2AC,$ the coefficient of friction is given by $\mu =k\tan \theta$ ). The value of $k$ is _________

Answer 1

Answer: 3

Apply work energy theorem
$mg\sin \theta (AC+2AC)-\mu mg\cos \theta AC=0$
$\mu =3\tan \theta$