A ring is hung on a nail. It can oscillate, without slipping or sliding (i) in its plane with a time period $T_1$ and (ii) back and forth in a direction perpendicular to its plane, with a period $T_2$. The ratio $\frac{T_1}{T_2}$ will be:\\
(1) $\frac{2}{\sqrt{3}}$\\
(2) $\frac{2}{3}$\\
(3) $\frac{3}{\sqrt{2}}$\\
(4) $\frac{\sqrt{2}}{3}$