C$.6$ A uniform rectangular gate $AB,$ of $2m$ wide and $3m$ long is located at the exit of a water tank as shown in Fig. C$\mathrm{.}6.$ The gate is hinged at A and rested against a smooth floor. The depth of water inside the tank is $5m$ while $1\mathrm{.}2m$ at outside.

$($a$)$ Calculate the magnitude of the hydrostatic force against the gate inside the water tank and its perpendicular distance to the hinge at A$.$

$(9$ marks$)$

$($b$)$ Calculate the magnitude of the hydrostatic force against the gate outside the water tank and its perpendicular distance to the hinge at A$.$

$(8$ marks$)$

$($c$)$ Estimate the minimum self$-$weight of the gate required to keep the gate close, using the above results or otherwise.

$(3$ marks$)$

Fig. C$.6$