# A circular disc rotates freely about a vertical axis through its centre with angular velocity $\omega_1$ . A ring having the same mass and radius as the disc is placed on the disc and the system now rotates with an angular velocity $\omega_2$ about the same vertical axis. Then $\omega_2 / \omega_1$ is

$\begin {array} {1 1} (1)\;\large\frac{1}{3} & \quad (2)\;\large\frac{1}{2} \\ (3)\;\large\frac{3}{2} & \quad (4)\;\large\frac{2}{3} \end {array}$

(1) $\large\frac{1}{3}$