A circular table is rotating with an angular velocity of ω rad / s about its axis (see figure). There is a smooth groove along a radial direction on…

A circular table is rotating with an angular velocity of $\displaystyle \omega \mathrm{rad} / \mathrm{s}$ about its axis (see figure). There is a smooth groove along a radial direction on the table. A steel ball is gently placed at a distance of $\displaystyle 1$ m on the groove. All the surfaces are smooth. If the radius of the table is $\displaystyle 3$ m , the radial velocity of the ball w.r.t. the table at the time ball leaves the table is $\displaystyle x \sqrt{2} \omega \mathrm{~m} / \mathrm{s}$, where the value of $\displaystyle x$ is $\displaystyle \_\_\_\_$.