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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 by the block to slide equal distances on rough incline is n times as much to slide on smooth incline of same angle of inclination. Then 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 A

μk=11n2


S=12gsin45t2.......(1)
For rough inclined plane
S=12[gsin45μgcos45]t2n2......(2)
[a=gsinθμgcosθ where θ=45]
By (1) and (2)
g2×12t2=g2[12μ2]n2t212=(1μ)2n21n2=1μμ=11n2


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