question_answer

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) \[\frac{W}{2\sqrt{3}}\]

Correct Answer: D

Solution :

[d] \[2N\cos 30{}^\circ =W.\] \[N=\frac{W}{\sqrt{3}}\] \[\text{and }N\sin 30{}^\circ =F\] \[\text{or }\frac{W}{\sqrt{3}}\times \frac{1}{2}=F,\text{ or F=}\frac{W}{2\sqrt{3}}.\]