Question

One fourth length of a uniform rod is placed on a rough horizontal surface and rod starts rotating about the edge. At an angle $\theta$ between the rod and the horizontal, rod begins to slide on the edge. If coefficient of friction between rod and surface is $\mu$ and 13 tan $\theta =x\left(\mu \right).$ Find x. (Take g$=10m/s^2)$

• A. 4
• B. 8
• C. 2
• D. 6

Answer 1

The correct option is A 4

$\frac{mgl}{4}sin\theta =\frac{1}{2}I{\omega }^2$
$\alpha =\frac{mg\frac{l}{4}cos\theta }{I}$
$\mu N-mgsin\theta =m{\omega }^2\frac{l}{4}$
$mgcos\theta -N=m\frac{l}{4}\alpha$
Solving,
$13tan\theta =4\mu .$