JEE Main 2024 — Rotational Motion Question with Solution

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 _________.