$1.$ A piston having a cross$-$sectional area of $0\mathrm{.}09m^2$ is located in a cylinder containing water as shown below. An open U$-$tube manometer is connected to the cylinder as shown. For $h_1=40mm$ and $h=100mm,$ what is the value of the applied force, $P,$ acting on the piston? The weight of the piston is negligible. If you are a bit confused, Newton's third law of motion might help get you started.

$2.$The uniform control gate $AB$ is pinned at A and rests on the smooth surface at $B.$ If the gate has a mass of $7\mathrm{.}50Mg,$ determine the maximum depth of water $h$ in the reservoir that will cause the gate to be on the verge of opening. The gate has a width of $1m.$

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