d
\(\begin{array}{l}
N\,\sin \,\theta  = m\frac{r}{2}{\omega ^2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( i \right)\\
N\,\cos \,\,\theta  = mg\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( {ii} \right)\\
\tan \,\,\theta \, - \frac{{r{\omega ^2}}}{{2g}}\\
\frac{r}{{2\frac{{\sqrt 3 \,r}}{2}}} = \frac{{r{\omega ^2}}}{{2g}}\,\,\,;\,\,{\omega ^2} = \frac{{2g}}{{\sqrt 3 \,r}}
\end{array}\)