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
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
$µ = sin$$\theta$
$µ = cot$$\theta$
$µ = 2\, cos$$\theta$
$µ = 2 \,tan$$\theta$
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
For upper half
${v^2} = {u^2} + 2al/2 = 2(g\sin \theta )l/2 = gl\sin \theta $
For lower half
$⇒$ $0 = {u^2} + 2g(\sin \theta - \mu \cos \theta )\frac{l}{2}$
$⇒$ $ - gl\sin \theta = gl(\sin \theta - \mu \cos \theta )$
$⇒$ $\mu \cos \theta = 2\sin \theta \Rightarrow \mu = 2\tan \theta $
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