    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=1−1n2For Smooth surface, ma=mgsinθ⇒a=gsinθhere, time =t and distance=d, so using formula S=ut+12at2, we getd=0+12(gsinθ)t2 ( initially block is at rest so u=0)∴d=12(gsinθ)t2......(1)For rough surface, ma=mgsinθ−f=mgsinθ−μmgcosθ⇒a=gsinθ−μgcosθhere, time=nt so,d=12(gsinθ−μgcosθ)(nt)2.....(2)(2)/(1),1=(gsinθ−μgcosθ)(nt)2(gsinθ)t2put θ=45,1=(1√2−μ1√2)n21√2or,(1−μ)n2=1∴μ=1−1n2   Suggest Corrections  0      Similar questions  Related Videos   PHYSICS
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