The upper half of an inclined plane of inclination θ is perfectly smooth while the lower half is rough. A body starting from the rest at the top comes back to rest at the bottom if the coefficient of

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The upper half of an inclined plane of inclination θ is perfectly smooth while the lower half is rough. A body starting from the rest at the top comes back to rest at the bottom if the coefficient of friction for the lower half is given by

TestHub · Accepted Answer

For the upper half v 2 = u 2 + 2 al / 2 = 2 ( gsinθ ) l / 2 = glsinθ For lower half ⇒ 0 = u 2 + 2 g ( sinθ − μcosθ ) l 2 ⇒ − glsinθ = gl ( sinθ − μcosθ ) ⇒ μcosθ = 2 sinθ ⇒ μ = 2 tanθ

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