The Young's modulus of a rubber string of length $$12 \mathrm{~cm}$$ and density $$1.5 ~\mathrm{kgm}^{-3}$$ is $$5 \times 10^8 ~\mathrm{Nm}^{-2}$$. When this string is suspended vertically, the increase in its length due to its own weight is (Take, $$g=10 \mathrm{~ms}^{-2}$$ )