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Question

A smooth block is released at rest on a 45o 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 D μk=11n2
On a rough surface
a=(gsinθμgcosθ)
time=nt
S=ut+12at2

0+12[gsinθμgcosθ](nt)2 ....(1)

On plane surface
a=gsinθ
time = t

S=0+12(gsinθ)t2 ...(2)

By solving (1) and (2)
μ=11n2 [μ=μk has the body is moving]

Hence (A) is corrct answer




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