A turn-table is rotating about its center with an angular velocity of $2 \mathrm{rad} / \mathrm{s}$ in the counter-clockwise direction. There is a groove in the turn-table within which a marble moves with a constant speed $v \mathrm{~m} / \mathrm{s}$ relative to the turn-table. At a given instant, the marble is at a radial distance of $1$ m from the center and the line joining the center of the turn-table with the marble makes an angle of $30^{\circ}$ with the groove. The value of $v$ $\text{(in $\mathrm{m} / \mathrm{s}$, rounded off to one decimal place)}$ for which there is no radial acceleration for the marble at this instant is ____________.
