The uniform control gate $AB$ shown in $($Figure $1)$ is pinned at A and rests on the smooth surface at $B.$ The gate has a width of

$1$ m $.$ Take ${}_w=1000k\frac{g}{m^3}.$

Figure

Part A

If the gate has a mass of $12\mathrm{.}4$ Mg $,$ determine the maximum depth of water $h$ in the reservoir that will cause the gate to be on the

verge of opening.

Express your answer to three significant figures and include the appropriate units.