(Suppose $\ell$ is distance of point of pivoting from $COM$)

$=2 \pi \sqrt{\frac{\left(\frac{m R^{2}}{2}+m \ell^{2}\right)}{m g \ell}}=2 \pi \sqrt{\frac{R^{2}+2 \ell^{2}}{2 g \ell}}$

$L_{eff}=\frac{R^{2}+2 \ell^{2}}{\ell}$ should be minimum for $T$ to be minimum

$\frac{d L_{e f f}}{d l}=\frac{\ell(+4 \ell)-\left(R^{2}+2 \ell^{2}\right)}{\ell^{2}}=0$

$4 \ell^{2}-K^{2}-2 \ell^{2}=0$

$\mathrm{R}^{2}-2 \ell^{2}$

$\frac{R}{\sqrt{2}}=\ell$