Dominant peg

A semicircular wire of radius \(r\) is supported in its own vertical plane by a hinge at \(O\) and smooth peg \(P\) as shown. If peg starts from \(O\) and moves with constant speed \(v\) along horizontal axis through \(O\). The angular speed of wire at time \(t\) is of the form \(\frac{m}{n}\), where \(m\) and \(n\) are coprime positive integers. Find \(\sqrt [ m ]{ n } \).

Details

\(r=5 \text{ m}, v=3 \text{ms}^{-1}, t=2\text{ s}\).

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