Rotational Motion

A circular table is rotating with an angular velocity of \(\omega \mathrm{~rad} / \mathrm{s}\) 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 \(1 \mathrm{~m}\) on the groove. All the surfaces are smooth. If the radius of the table is \(3 \mathrm{~m}\), the radial velocity of the ball w.r.t. the table at the time ball leaves the table is \(x \sqrt{2} \omega \mathrm{~m} / \mathrm{s}\), where the value of \(x\) is _________.