At critical condition at \(C\)

\(v=\sqrt{g R}\)

Using mechanical energy conservation between points \(P\) and \(C\) (taking P.E. \(=0\) at \(P\) )

\(U_i+k_i=U_f+k_f\)

\(0+\frac{1}{2} m v^2=m g R\left(1-\cos 60^{\circ}\right)+\frac{1}{2} m(\sqrt{g R})^2\)

\(\frac{1}{2} m v^2=\frac{m g R}{2}+\frac{m g R}{2}\)

\(v=\sqrt{2 g R}\)