An aluminium wire is wound on a piece of cork of mass 10 g. The densities ${\text{ρ}}_c,{\rho }_a and {\rho }_w$of cork, aluminium and water are $0.5\times {10}^3 \mathrm{kg}/{\mathrm{m}}^3, 2.7\times {10}^3 \mathrm{kg}/{\mathrm{m}}^3 \mathrm{and} 1\times {10}^3 \mathrm{kg}/{\mathrm{m}}^3$ respectively. The minimum mass of aluminium wire that should be wound on the cork so that the cork with the wire should stay completely submerged in water is: