# 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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