A body is moving down a long inclined plane of angle of inclination θ. The coefficient of friction between the body and the plane varies as μ $$=$$ $$0.5$$ x, where x is the distance moved down the plane. The body will have the maximum velocity when it has travelled a distance x given by

Question

A body is moving down a long inclined plane of angle of inclination θ. The coefficient of friction between the body and the plane varies as μ $$=$$ $$0.5$$ x, where x is the distance moved down the plane. The body will have the maximum velocity when it has travelled a distance x given by

Infinity Learn · Accepted Answer

The acceleration of the body down the plane is gsin⁡θ−μgcos⁡θ$$=g($$$$sin$$⁡θ−μ$$cos$$⁡θ$$)=g($$$$sin$$⁡θ$$-0.5xcos$$⁡θ$$)$$. Therefore, the body will first accelerate up to x < $$2$$ $$tan$$ θ. The velocity will be maximum at x $$=$$ $$2$$ $$tan$$ θ, because for x > $$2$$ $$tan$$ θ, the body starts decelerating. Hence, the correct choice is (a).

A body is moving down a long inclined plane of angle of inclination $θ$ . The coefficient of friction between the body and the plane varies as $μ$ = 0.5 x, where x is the distance moved down the plane. The body will have the maximum velocity when it has travelled a distance x given by

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A body is moving down a long inclined plane of angle of inclination θ. The coefficient of friction between the body and the plane varies as μ = 0.5 x, where x is the distance moved down the plane. The body will have the maximum velocity when it has travelled a distance x given by

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Ready to Test Your Skills?

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A body is moving down a long inclined plane of angle of inclination $θ$ . The coefficient of friction between the body and the plane varies as $μ$ = 0.5 x, where x is the distance moved down the plane. The body will have the maximum velocity when it has travelled a distance x given by