Problem $21$: A barge $($seen in Figure$)$ measuring $15m$ by $4m$ and $3m$ deep, has $900k\frac{g}{m^3}$

density. It carries a load of $150kN.$ The barge floats in sea water with a density of $1\mathrm{.}090$

$k\frac{g}{m^3}.$

a$)$ Find the barges sinking depth.

b$)$ Find it's metacentric height and determine the stability of barge if it moves sideway with

$6$ angular tilt.

c$)$ Find the change in moment of the buoyoncy force.