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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. The coefficient of kinetic 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 a=gsinθ Acceleration with friction af=gsinθ−μgcosθ Now time taken t=√2ha where h is the vertical distance down the inclined plane, which doesn't change. Thus, TTf=√afa =√gsinθ−μgcosθgsinθ =√1−μcotθ Given Tf=2T ⇒12=√1−μcotθ ⇒14=1−μcotθ ⇒1−14=μcotθ 34=μcot45∘=μ ∴μ=34=0.75

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