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Question

A smooth block is released at rest from 45 incline slides a distance d. The time taken to slide is n time as much to slide on a rough incline plane than on a smooth incline. Find the coefficient of friction.

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

The correct option is B μk=11n2
For Smooth surface, ma=mgsinθa=gsinθ
here, time =t and distance=d, so using formula S=ut+12at2, we get
d=0+12(gsinθ)t2 ( initially block is at rest so u=0)
d=12(gsinθ)t2......(1)
For rough surface,
ma=mgsinθf=mgsinθμmgcosθa=gsinθμgcosθ
here, time=nt so,
d=12(gsinθμgcosθ)(nt)2.....(2)
(2)/(1),1=(gsinθμgcosθ)(nt)2(gsinθ)t2
put θ=45,
1=(12μ12)n212
or,(1μ)n2=1
μ=11n2
151325_135935_ans_757df013436a4479bf7fce5dd8aff647.png

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