The upper half of an inclined plane of inclination $ heta$ is perfectly smooth while the lower half is rough. A body starting from the rest at top comes back to rest at the bottom if the coefficient of friction for the lower half is given by

Question

The upper half of an inclined plane of inclination $	heta$ is perfectly smooth while the lower half is rough. A body starting from the rest at top comes back to rest at the bottom if the coefficient of friction for the lower half is given by

Dr. Abubacker · Accepted Answer

(d) For upper half
$v^{2} = u^{2} + 2al/2 = 2\left( g\sin	heta ight)l/2 = gl\ sin\ 	heta$
For lower half
$\Rightarrow 0 = u^{2} + 2g(\sin{	heta - \mu\cos	heta)\ \frac{l}{2}}$
$\Rightarrow - gl\sin	heta = gl(\sin	heta - \mu\cos	heta)$
$\Rightarrow \mu\cos	heta = 2\sin	heta \Rightarrow \mu = 2	an	heta$

Q. The upper half of an inclined plane of inclination $\theta$ is perfectly smooth while the lower half is rough. A body starting from the rest at top comes back to rest at the bottom if the coefficient of friction for the lower half is given by

Explanation

Reviewed by Dr. Abubacker

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