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Classical Mechanics Level 5

A triangular loop \(ABC\) of light string is passed over two small frictionless pulleys A and B \( (AB = BC = AC = 2l)\)

Two masses \(m\) and \( M\) are attached at the midpoint \(O\) of \(AB\) and at point \(C\), respectively. If \(m\) is released, \(m\) & \(M\) cross each other at any point \( P\) as shown in the figure. Find the minimum value of \(\dfrac {m}{M}\) so that they cross each other.

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