FrictionHard

Question

The upper portion of an inclined plane of inclination a is smooth and the lower portion is rough. A particle slides down from rest from the top and just comes to rest at the foot. If the ratio of the smooth length to rough length is m : n, the coefficient of friction is :

Options

A. tan α
B. tan α
C. tan α
D.

Solution


On smooth surface a1 = g sin α
∴ v2 = u2 + 2a1s1
= 0 + 2 g sin a .m
On rough surface
a2 = g sin α − mg cos a
∴ v′2 = v2 + 2a2s2
O = 2mg sin α + 2g (sin α − μ cos α)n
⇒    μ = tan α

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