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

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