A standard cell of $1.08\mathrm{ }\mathrm{V}$ is balanced by the potential difference across $90\mathrm{ }\mathrm{c}\mathrm{m}$ of a $1$ meter, long wire supplied by a cell of emf $2\mathrm{V}$ through a series resistor of resistance $2\mathrm{ }\mathrm{\Omega }$. If the internal resistance of cell in the primary circuit is zero then the resistance per unit length (in $\mathrm{\Omega } {\mathrm{m}}^{-1}$) of potentiometer wire is