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. $\frac{2\,tan\,\theta}{\mu_{0}}$

Answer 1

Answer: (C)

Acceleration of mass at distance $x$,
$a=g (sin\,\theta-\mu_0\,x\,cos\,\theta)$
Speed is maximum, when $a = 0$
$\Rightarrow g (sin \,\theta-\mu_{0}\,x\,cos\,\theta)=0$
$\therefore x=\frac{tan\, \theta}{\mu_{0}}$