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Question

A body is moving down an inclined plane of slope $$\displaystyle 37^{\circ}.$$ The coefficient of friction between the body and the plane varies as $$\displaystyle \mu = 0.3 x,$$ where x is the distance traveled down the plane by the body. The body will have maximum speed. $$\displaystyle \left ( \sin 37^{\circ}= \frac{3}{5}  \right )$$


A
at x=1.16m
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B
at x=2m
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C
at bottommost point of the plane
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D
at x=2.5m
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Solution

The correct option is C at x=2.5m
velocity will be maximum when $$\dfrac{dv}{dt}=0$$. i.e $$a=0$$
$$gsin\theta = \mu g cos\theta$$
$$tan\theta = \mu =0.3x = 0.75$$
$$x = 2.5$$ m

Physics

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