# Give me ID Card-2!

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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