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