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

from work energy theorem
$W_g+W_f=\Delta kE$
$mg3x\sin \theta -\mu mg\cos \theta x=0-0$
$\Rightarrow mg3x\sin \theta =\mu mg\cos \theta x$
$3\tan \theta =\mu$
$k=3$