$($Force on plane surface$)$ The rectangular gate CD of the figure below is $1\mathrm{.}6$ m wide and $2\mathrm{.}0$ m long. Assuming the

material of the gate to be homogeneous and neglecting friction at the hinge $C,$ determine the weight of the gate

necessary to keep it shut until the water level rises to $1\mathrm{.}8$ m above the hinge.

$W=kN$