A uniform rectangular gate $AB$ of $2m$ long and $1m$ wide is rested at the exit of a water tank as shown in figure below. The gate is hinged at A and inclined at $60$ to horizontal. The depth of water inside the tank is $4m$ while $1\mathrm{.}5m$ at outside. Determine the self$-$weight of the gate in order to keep the gate close.