\(N \cos \left(90^{\circ}-\theta\right)=\frac{m v^2}{r}\)

\(N \sin \left(90^{\circ}-\theta\right)=m g\)

\(N=\frac{m g}{\cos \theta} \ldots (i)\)

and \(N \sin \theta=\frac{m v^2}{r} \ldots (ii)\)

dividing \((ii)\) and \((i)\)

\(m g \tan \theta=\frac{m v^2}{r}\)

\(g\left(\frac{h}{r}\right)=\frac{v^2}{r} \Rightarrow v=\sqrt{g h}\)