Question

The upper half of an inclined plane with inclination Φ 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​

Answer 1

Answer:

Suppose length of plane is L. When block descends the plane, rise in kinetic energy = fall in potential energy =mgLsinθi

Work done by friction =μ×(reaction)×distance 0+μ(mgcosθ)×(L/2)

=μ(mgcosθ)×(L/2)

Now, work done= change in KE

mgLsinθ=μ(mgcosθ)×(L/2)

⇒tanθ=μ/2

∴μ=2tanθ.

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