The upper half of an incline 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 the bottom if the coeffici…

Question

The upper half of an incline 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 the bottom if the coefficient of friction for the lower half is given by

Accepted Answer

Correct answer: A. (a) According to work-energy theorem, W - ΔK = 0 ( ∴Initial and final speed are zero) ∴ Work done by friction + work done by gravity = 0 – (μ mg cosφ) 2 + mgl λ sin φ = 0 ⇒ μ cos φ = 2 sin φ ⇒ μ = 2 tan φ

$The upper half of an incline plane with inclination φ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the the bottom if the coefficient of friction for the lower half is given by$

Solution

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