Question

# The upper half of an inclined plane with inclination θ 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, then the coefficient of kinetic friction for the lower half is given by

A
2 tan θ
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B
tan θ
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C
2 sin θ
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D
2 cos θ
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Solution

## The correct option is A 2 tan θ For first half, acceleration =gsinθ ∴v2=2(gsinθ)l .......(1) For second half, acceleration =g(sinθ−μkcosθ) 0=v2+2g(sinθ−μkcosθ)l ....(2) Putting equation (1) in equation (2), we get: 0=(2gsinθ)l+(2gsinθ)l−(2gμkcosθ)l ∴μkcosθ=2sinθ or μk=2tanθ Hence, the correct answer is option (a).

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