The concrete gravity dam is designed so that its weight provides stability against overturning due to the pressure of the liquid. Under this state of equilibrium, the liquid pressure generates an overturning moment about point A and the dam weight develops a stabilizing moment about point A to guarantee the stability and safety of the dam. Considering that the liquid density is $1000$ kg$/$m$3$ and concrete density is $2400$ kg$/$m$3,$ and the dam does not slide,

a$)$ Draw the FBD of the concrete dam.

b$)$ Find the minimum dimension b so that the ratio of the stabilizing moment to the overturning moment $($both taken about point A$)$ is $2.$