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 modulus Y = 2 $\times$ 10¹¹ Nm^$-$2 and g = 10 ms^$-$2)