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A small mass slides down a fixed inclined plane of inclination $θ$ with the horizontal. The coefficient of friction is $μ = μ_{0} x$ where $x$ is the distance through which the mass slides down and $μ_{0}$ is a constant. Then the speed is maximum after the mass covers a distance of

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$\frac{\cos θ}{μ_{0}}$

$\frac{\sin θ}{μ_{0}}$

$\frac{\tan θ}{μ_{0}}$

$\frac{2 \tan θ}{μ_{0}}$

answer is C.

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Detailed Solution

Acceleration of mass at distance x, $a = g (\sin θ - μ_{0} x \cos θ)$

Speed is maximum, when a=0, $g (\sin θ - μ_{0} x \cos θ) = 0$

$x = \frac{\tan θ}{μ_{0}}$

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