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  4. Two smooth cylindrical bars weighing W N 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

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Q. Two smooth cylindrical bars weighing $W N$ 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 isPhysics Question Image

Laws of Motion

Solution:

For upper cylinder
image
$2 N \cos 30^{\circ}=W$ ...(i)
For lower block
$N \cos 60^{\circ}=F$ ...(ii)
From (i) & (ii)
$\frac{2 \cos 30^{\circ}}{\cos 60^{\circ}}=\frac{W}{F}$
$\Rightarrow F=\frac{W}{2 \sqrt{3}}$