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# The upper half of an inclined plane with an inclination a, 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 is given by:

Asked by Arushi Juyal 12th November 2017, 5:00 PM
Refer the diagram above.  For upper half which is smooth, the acceleration is g×sin(a).
Since the object starts from rest the final velocity when it reaches the end of upper half
is √( g×l×sin(a) ).

For the lower part the acceleration is ( g×sin(a) - μ×g×cos(a) ) due to friction

Since the oblect comes to rest when it reaches the bottom of inclined plane
we use the relation " u2 + 2αs = 0 ", where α is acceleration.

Hence ( g×l×sin(a) ) = -2 ( g×sin(a) - μ×g×cos(a) ) (l/2)

Solving for μ we will get μ = 2 × tan(a)
Answered by Expert 13th November 2017, 3:27 PM
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