$($c$)$ A barge designed to carry grain along a canal can be assumed to have uniform density with a specific gravity of $0\mathrm{.}70.$ The barge is $20\mathrm{.}0m$ long and can be regarded as having a distance from keel to top of $3\mathrm{.}60m.$ What is the minimum width of the barge for it to be stable against capsizing in its roll direction? Assume water in the canal has a density of $1\mathrm{.}025k\frac{g}{m^3}$

$(15$ marks$)$