Two beads of mass \(m\) each are positioned at the top of a frictionless hoop of mass \(M\) with radius \(R\) , which stands vertically on the ground. The beads are given a slight push, and they slide down the hoop, one to the right and the other one to the left, as shown . What is the smallest value of \[\frac{m}{M}\] for which the hoop will rise up off the ground at some time during the motion?

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