A uniform steel rod of mass $1.8 \mathrm{~kg}$ and length $0.8 \mathrm{~m}$ is hung from a nail with the help of a steel wire of area of cross-section $0.01 \mathrm{~mm}^2$ and unstretched length of $1 \mathrm{~m}$ as shown in the figure. The centre of mass of the rod lies vertically below the nail. The increase in the distance between the centre of mass of the rod and the nail due to stretching of the wire as the rod hungs is ____ $\mathrm{mm}$.
(Young's modulus of steel $=2 \times 10^{11} \mathrm{Nm}^{-2}$ and acceleration due to gravity $=10 \mathrm{~ms}^{-2}$)