Question

A small mass slides down an inclined plane of inclination $\theta$ with the horizontal. The coefficient of friction is $\mu ={\mu }_0$ $x$ where $x$ is the distance through which the mass slides down and ${\mu }_0$, a constant. Then the speed is maximum after the mass covers a distance of

• A. $\frac{cos\theta }{{\mu }_0}$
• B. $\frac{sin\theta }{{\mu }_0}$
• C. $\frac{tan\theta }{{\mu }_0}$
• D. $\frac{2tan\theta }{{\mu }_0}$

Answer 1

Answer: (C)

Acceleration of mass at distance $x$,

$a=g(sin\theta -{\mu }_{0}xcos\theta )$

Speed is maximum, when $a=0$

$\Rightarrow g(sin\theta -{\mu }_{0}xcos\theta )=0$

$\therefore x=\frac{tan\theta }{{\mu }_0}$