Question

A body is moving down a long inclined plane of angle of inclination $\theta$. The coefficient of friction between the body and the plane varies as $\mu =0.5x$, 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

• A. $x=2tan\theta$
• B. $x=\frac{2}{tan\theta }$
• C. $x=\sqrt{2}cot\theta$
• D. $x=\frac{\sqrt{2}}{cot\theta }$

Answer 1

The correct option is A

$x=2tan\theta$

The acceleration of the body down the plane is $gsin\theta -\mu gcos\theta =g(sin\theta -0.5xcos\theta )$.
For velocity to be maximum, acceleration of the body should be zero.
$g(sin\theta -0.5xcos\theta )=0\Rightarrow sin\theta =0.5xcos\theta \Rightarrow x=2tan\theta$
Hence, the correct choice is (a).