A uniform rectangular gate $AB$ of $3m$ long and $1\mathrm{.}5m$ wide in Fig $05$ below

is hinged at A and inclined at $40$ to horizontal. The depth of diesel oil on the

left side of the gate is $5m.$ The depth of seawater on the right side of the

gate is $1\mathrm{.}5m.$ Determine the self$-$weight of the gate in order to keep the gate

closed. The density of seawater is $1025k\frac{g}{m^3}$ and the density of diesel

oil is $875k\frac{g}{m^3}.$

Fig. $05$