Question

Three identical rigid circular cylinders $A, B$ and $C$ are placed on smooth inclined plane shown in the figure. The minimum value of $\tan \theta$ that prevent the arrangement from collapse is $\frac{1}{3 \sqrt{n}}$. The value of $n$ is___.

Answer 1

From free body diagram of cylinder $A, 2 N \cos 30^{\circ}=m g$
$\therefore N=\frac{m g}{\sqrt{3}}$

From free body diagram of cylinder $B$,
$N_{0} \cos \theta \equiv mg + N \cos 30^{\circ}, $
$N_{0} \sin \theta=N \sin 30^{\circ}$
$\tan \theta=\frac{N \sin 30^{\circ}}{m g+N \cos 30^{\circ}}$

Putting the value of $N, \tan \theta=\frac{1}{3 \sqrt{3}}$
$\therefore n=3$