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 The gate is hinged at A and

rested against a smooth floor. The depth of water inside the tank is $7m$

while $0\mathrm{.}8m$ 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$.$

$($b$)$ Calculate the magnitude of the hydrostatic force against the gate

outside the water tank and its perpendicular distance to the hinge at

A$.$

$($c$)$ Estimate the minimum self$-$weight of the gate required to keep the

gate close, using the above results or otherwise.

Fig. C