QUESTION $3$

A $2\mathrm{.}5$ m$-$wide rectangular inclined plate is hinged at point $\backslash ($ A $\backslash )$ and is held by a cable at point $\backslash ($ B $\backslash )$ to retain oil $($S$.$G$.$oil $\backslash (=0\mathrm{.}86\backslash ))$ in a tank as shown in Figure Q$3.$

i$.$ Illustrate a free$-$body diagram representing the forces and moments acting on the inclined plate.

ii$.$ Calculate the resultant hydrostatic force, $\backslash (\backslash$mathrm$\{$F$\}\_\{\backslash$mathrm$\{$R$\}\}\backslash )$ exerted by the fluid on the inclined plate and determine the position of its center of pressure, $\backslash (\backslash$mathrm$\{$h$\}\_\{\backslash$mathrm$\{$cp$\}\}\backslash ).$

iii. Determine the tension, T in the cable when the tank is filled with oil to the top. $($note: the length of the inclined plate is $3$m$)$

Figure Q$3$

CO$2/$PO$2/$C$4/$DK$4(15$ marks$)$