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

Answer: 3

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

From free body diagram of cylinder $B$,
$N_0\cos \theta \equiv mg+N\cos 30^{\circ },$
$N_0\sin \theta =N\sin 30^{\circ }$
$\tan \theta =\frac{N\sin 30^{\circ }}{mg+N\cos 30^{\circ }}$

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