A given object takes n times more time to slide down 45∘ rough inclined plane as it takes to slide down a perfectly smooth 45∘ incline. The coefficient of kinetic friction between the object and the incline is
From s=ut+12at2=0+12at2,t=√2sa
For smooth plane a=gsin θ
For rough plane, a′=g(sin θ−μcos θ)
∴t′=nt⇒√2sg(sin θ−μcos θ)=n√2sgsin θ
∴n2g(sin θ−μcos θ)=gsin θ
When gsin θ=45∘,sin θ=cos θ=1√2
Solving, we get μ=11−n2