A $3^{\text{'}}$ long, $2^{\text{'}}$ wide $($into$-$the$-$page$)$ rectangular plate is

attached to the bottom of a water reservoir by a hinge to form

a drain$-$gate. One end of a cable is attached to the middle of

the gate and the other to a counterweight. If the gate is to

open when the fluid fills to a depth of $7^{\text{'}},$ what mass

counterweight is required?

For a rectangular plate, $I_{xC}=\frac{1}{12}b{h}^3.$