A block, released from rest from the top of a smooth inclined plane of inclination θ, has a speed v when it reaches the bottom. The same block, released from the top of a rough inclined plane of the same inclination θ, has a speed $$v/n$$ on reaching the bottom, where n is a number greater than unity. The coefficient of friction is given by

Question

A block, released from rest from the top of a smooth inclined plane of inclination θ, has a speed v when it reaches the bottom. The same block, released from the top of a rough inclined plane of the same inclination θ, has a speed $$v/n$$ on reaching the bottom, where n is a number greater than unity. The coefficient of friction is given by

Infinity Learn · Accepted Answer

We use the relation $$v2$$−$$u2=2as$$. Since u $$=$$ $$0$$, we have $$v2=2as$$.Now $$v12=2a1s$$ or $$v2=2g$$ $$sin$$⁡θ×sand $$v22=2a2s$$ or $$v2n2=2(gsin$$⁡θ−μgcos⁡θ$$)$$×sDividing, we get  $$n2($$$$sin$$⁡θ−μ$$cos$$⁡θ$$)=$$$$sin$$⁡θwhich gives μ$$=1$$−$$1n2tan$$⁡θ, which is choice (1).

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