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