Question

Two smooth cylindrical bars weighing $W$ each, lie next to each other in contact. A similar third bar is placed over the two bars as shown in figure. Neglecting friction, the minimum horizontal force on each lower bar necessary to keep them together is

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

Answer 1

The correct option is D $\frac{W}{2\sqrt{3}}$



Weight of the cylinder placed on the top is balanced by the vertical component of normal reaction acting on it from both the cylinders below.
The free body diagram of top cylinder is given as


$2N\cos {30}^o=W$
$⟹N=\frac{W}{\sqrt{3}}$

For the cylinders lying on the ground:
$N\sin {30}^o=F$
or $\frac{W}{\sqrt{3}}\times \frac{1}{2}=F$
or $F=\frac{W}{2\sqrt{3}}$