Stack them up!

Two smooth cylindrical bars weighing \(20\sqrt { 3 } N\) each lie next to each other in contact. A similar third bar is placed over the two bars as shown in the figure.

To keep the bottom two cylinders in contact equal and opposite horizontal forces are applied at the centers of both the bottom cylinders.

If the friction is neglected, what is the minimum horizontal force on one of the cylinders required to keep them in contact?

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