Three weightless rods of length \(l\) each are hinged at point \(A\) and \(B\) lying on the same horizontal and joint through hinges at points \(C\) and \(D\) (shown below).

The length \(A\)\(B\) \(=\) \(2\)\(l\). A load of mass \(m\) is suspended at hinge \(C\).Determine the minimum force \(F\) applied to the hinge \(D\) for which the middle rod remains horizontal.

If \(F\) can be described as \(\dfrac{mg}{k}\), determine \(k\)

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