Question

Three identical cylinders are kept touching each other as shown in figure. Coefficient of friction between cylinder and surface is $\mu$ whereas, between the cylinders is zero. The minimum value of $\mu$ so that system remains in equilibrium is

• A. $\frac{1}{3}$
• B. $\frac{1}{\sqrt{3}}$
• C. $\frac{1}{3\sqrt{3}}$
• D. $\frac{1}{2\sqrt{3}}$

Answer 1

The correct option is C $\frac{1}{3\sqrt{3}}$


In the FBD of A, balancing the forces in y direction gives,

$2N_A\cos 30=mg$

$\Rightarrow N_A=\frac{mg}{\sqrt{3}}$
In the FBD of B,

$N_B=N_A\cos 30+mg$ --- (1) $N_A\sin 30=f$ --- (2)
$f=\mu N_B$ -- (3)
From (1), (2) and (3),
$\mu =\frac{1}{3\sqrt{3}}$