Getting back to the old things #6

A solid body of mass \(M\) is in the shape of a quadrant sphere of radius \(R\). It is released from rest in a position such that the curved portion is at a height \(R\).

The collision is perfectly elastic. The angular velocity of the body just after striking the ground is represented in the form \(\dfrac{a}{b} \sqrt{\frac{cg}{R}}\), where \(g\) represents acceleration due to gravity. Here \(a\) and \(b\) are coprime positive integers and \(c\) is square free.

Submit your answer as \(a+b+c\).

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