# 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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