$11-9$E $\backslash ($ A $\backslash )$ long, solid cylinder of radius $2$ ft hinged at point $\backslash ($ A $\backslash )$ is used as an automatic gate, as shown in Fig. P$11-9$E$.$ When the water level reaches $15$ ft $,$ the cylindrical gate opens by turning about the hinge at point $\backslash ($ A $\backslash ).$ Determine $($a$)$ the hydrostatic force acting on the cylinder and its line of action when the gate opens and $($b$)$ the weight of the cylinder per ft length of the cylinder.