Buoyancy = No Leakage of water !

The figure here shows a water tank provided with a square gate (of side \(2\text{ m}\)) which can rotated freely about \(z\) axis passing through shown point \(A\). The gate is held in its place due to buoyant force acting on the light balloon attached to the gate via a light thread. Considering the information that the gate just opens when level of water reaches the height of \(4 \text{ m}\) above point \(A\) and hinge force is zero, the shown point \(P\) is point at which the thread is attached to the gate

\((A)\) Volume of water displaced by the balloon is \(20 \text{ m}^3\).

\((B)\) Volume of water displaced by the balloon is \(30 \text{ m}^3\).

\((C)\) Distance between A and P is approximately \(1.06 \text{ m}\).

\((D)\) Force on gate due to Water is \(15 \text{ kN}\)

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