Question

The upper half of an inclined plane with inclination phi 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 the length of the 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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