A uniform heavy rod of mass $20 \mathrm{kg}$. Cross sectional area $0.4{ \mathrm{m}}^2$ and length $20 \mathrm{m}$ is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is $x\times {10}^{-9} \mathrm{m}$. The value of $x$ is _____ .
(Given. Young's modulus $Y=2\times {10}^{11}{\mathrm{Nm}}^{-2}$ and $g=10 \mathrm{m} {\mathrm{s}}^{-2}$ )