Pr $2$: The semicircular plane gate $AB$ is hinged at $B$ and held by the force, $F_A.$ The moment of inertia

about the centroidal axis is $\frac{}{4}{R}^4.$ Centroid can be found in tables below.

$($a$)$ Determine the depth of the centroid of the gate.

$($b$)$ Compute the net resultant force of the water on the gate.

$($c$)$ Compute depth of the center of pressure of the gate.

$($d$)$ Draw the FBD of all forces acting on the gate with all relevant dimensions.

$($e$)$ Compute the force, $F_A$ required to hold the gate in place.

$($f$)$ Compute the reaction force at $B.$