Question

A body of mass ' $m$ ' is launched up on a rough inclined plane making an angle of $30^{\circ }$ with the horizontal. The coefficient of friction between the body and plane is $\frac{\sqrt{x}}{5}$ if the time of ascent is half of the time of descent. The value of $x$ is_______.

Answer 1

Answer: 3

$t_a=\frac{1}{2}{t}_d$
$\sqrt{\frac{2s}{a_a}}=\frac{1}{2}\sqrt{\frac{2s}{a_d}}\dots \dots .$(i)
$a_a=g\sin \theta +\mu g\cos \theta$
$=\frac{g}{2}+\frac{\sqrt{3}}{2}\mu g$
$a_d=g\sin \theta -\mu g\cos \theta$
$=\frac{g}{2}-\frac{\sqrt{3}}{2}\mu g$
using the above values of $a_a$ and $a_d$ and putting ineqution (i) we will gate
$\mu =\frac{\sqrt{3}}{5}$