An object is placed on the surface of a smooth inclined plane of inclination θ. It takes time t, to reach the bottom. If the same object is allowed to slide down a rough inclined plane of inclination q, it takes time n t to reach the bottom where n is a number greater than one. The coefficient of friction μ is given by

Question

An object is placed on the surface of a smooth inclined plane of inclination θ. It takes time t, to reach the bottom. If the same object is allowed to slide down a rough inclined plane of inclination q, it takes time n t to reach the bottom where n is a number greater than one. The coefficient of friction μ is given by

Infinity Learn · Accepted Answer

For smooth inclined plane, acceleration $$=$$ g $$sin$$ qFor rough inclined plane, acceleration $$=gsin$$⁡θ−μgcos⁡θLet l be the length of inclined plane, then $$l=12(gsin$$⁡θ$$)t2$$  …(1)also$$ $$l=12(gsin$$⁡θ−μgcos⁡θ$$)(nt)2$$   …$$(2)∴ $$12(gsin$$⁡θ$$)t2=12(gsin$$⁡θ−μgcos⁡θ$$)(nt)2Solving$$, we getμ$$=$$$$tan$$⁡θ$$1$$−$$1n2$$.

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