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Question

# Starting from rest, a body slides down a 45∘ inclined plane in twice the time it takes to slide down the same distance in the absence of friction (with same inclination). The coefficient of friction between the body and the inclined plane is

A
0.33
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B
0.25
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C
0.75
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D
0.80
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Solution

## The correct option is C 0.75Acceleration without friction aw=g sinθ acceleration with friction af=g sinθ−μg cosθ Now time taken t=√2ha Let T time taken in the absence of friction, Tf time taken in the presence of friction. Given that Tf=2T ⇒TTf=√afaw=√gsinθ−mg cosθg sinθ ⇒12=√1−μcotθ Squaring on both sides and putting the value of cotθ=cot45∘=1, we get μ=34=0.75

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