A 4 - \(\mathrm{ft}\) by 3 - \(\mathrm{ft}\) massless rectangular gate is used to close the end of the water tank shown in Fig. P2.108. A 200-lb weight attached to the arm of the gate at a distance \(\ell\) from the frictionless hinge is just sufficient to keep the gate closed when the water depth is \(2 \mathrm{ft}\), that is, when the water fills the semicircular lower portion of the tank. If the water were deeper, the gate would open. Determine the distance \(\ell\).

Figure P2. 108

200 lb Gate- Hinge 1 ft Water Hinge /2 ft radius 4 ft 3 ft