Question

The upper half of an inclined plane with inclination $14^{\circ}$ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half $\mu=$____________ . (Take $\tan 14^{\circ}=0.25$ )

Answer 1

As, $v^{2}-u^{2}=2 a s$
In the journey over the upper hall of incline,
$v ^{2}-0=2( g \sin \theta) \frac{ s }{2}$
$v ^{2}= g \sin \theta s$
In the journey over the lower hall of incline,
$v ^{2}- u ^{2}=2$ as
$0- g s \sin \theta=2 g (\sin \theta-\mu \cos \theta) \frac{ s }{2}$
$-\sin \theta=\sin \theta-\mu \cos \theta$
$\therefore \mu=\frac{2 \sin \theta}{\cos \theta}$
$\therefore \mu=2 \tan \theta$
$=2 \tan 14^{\circ}$
$\therefore \mu=2 \times 0.25$
$\therefore \mu=0.5$