A $6$ m$-$high, $5m-$wide rectangular plate blocks the end of a $5m-$deep seawater channel $($salinity $35$ ppt$,S_g=1\mathrm{.}028,v=1\mathrm{.}15{10}^{-6}\frac{m^2}{s}).$ As shown in Figure $1,$ the plate is hinged about a horizontal axis along its upper edge, through point $A,$ and is restrained from opening by a fixed ridge on the channel floor, at point $B.$

$($a$)$ What is the mass density, specific weight, and absolute viscosity of this fluid? $[6$ marks$]$