A $3\mathrm{.}700-$m$-$long quarter$-$circular gate of radius $3$ m and of negligible weight is hinged about its upper edge $A,$ as shown in the figure. The gate controls the flow of water over the ledge at $B,$ where the gate is pressed by a spring. Determine the minimum spring force required to keep the gate closed when the water level rises to $A$ at the upper edge of the gate. Take the density of water to be $1,000k\frac{g}{m^3}.$

The minimum spring force required to keep the gate closed is $q,$ kN $.$