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 $BC =2 AC ,$ the coefficient of friction is given by $\mu= k \tan \theta$ ). The value of $k$ is _________

Answer 1

Apply work energy theorem
$m g \sin \theta(A C+2 A C)-\mu m g \cos \theta A C=0$
$\mu=3 \tan \theta$