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 $15 \text{ kN}$