The upper portion of an inclined plane of inclination α 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:
A
tan α
B
cot α
C
cot α
D
Text Solution
Verified by ExpertsThe correct answer is:
A
On smooth surface a 1 = g sin α
∴ v 2 = u 2 + 2a 1 s 1 = 0 + 2 g sin α .m
On rough surface a 2 = g sin α – μ g cos α
∴ v´ 2 = v 2 + 2a 2 s 2
O = 2mg sin α + 2g (sin α – µ cos α ) n
⇒ μ = 
tan α
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