A square plate is suspended vertically from one of its edges using a hinge support as shown in figure. A water jet of $20 \: mm$ diameter having a velocity of $10 \: m/s$ strikes the plate at its mid-point, at an angle of $30^{\circ}$ with the vertical. Consider $g$ as $9.81 \:m/s^2$ and neglect the self-weight of the plate. The force $F$ (expressed in $N$) required to keep the plate in its vertical position is _____________