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

Question

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

Infinity Learn · Accepted Answer

From s $$=$$ $$ut+12at2$$,$$t=2saFor$$ smooth plane a $$=$$ g $$sin$$ θ            For rough plane, a' $$=$$ $$g($$$$sin$$ θ $$-$$ μ $$cos$$ θ$$)t$$' $$=$$ nt⇒ $$2sg($$$$sin$$θ−μ$$cos$$θ$$)=n2sgsin$$θ$$n2g($$$$sin$$ θ $$-$$  μ$$cos$$ θ$$)$$ $$=$$ g $$sin$$ q            When θ $$=$$ $$45$$°, $$sin$$ θ $$=$$ $$cos$$ θ$$=$$ $$1/2Solving$$, we get μ$$=1$$−$$1n2$$

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

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