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Question

A smooth block is released at rest on a 45 incline and then slides a distance 'd'. The time taken to slide is 'n' times as much to slide on rough incline than on a smooth incline. The coefficient of friction is

A
μk=11n2
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B
μk=11n2
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C
μs=11n2
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D
μs=11n2
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Solution

The correct option is B μk=11n2

d=12(g sinθ)t1,

d=12(g sinθμg cosθ)t2

t1=2dg sinθ

t2=2dg sinθμg cosθ

According to question, t2=nt1

n2dg sinθ=2dg sinθμg cosθ

μ, applicable here, is kinetic friction as the block moves over the inclined plane.

n=11μk(cos 45=sin 45=12)

n2=11μk or 1μk=1n2

Or μk=11n2


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