The weight at any point x from below is, \(\frac {M}{10}\) (10 - x) where M is mass of string.

So, Force at any point dx is

F = \(\frac{Mg}{l}\) (l - x)dx

We know that,

Net extension =

So, Net extension of the rubber due to its own weight

= \(\frac{1.5 \times 10^3 \times 10 \times 100}{2 \times 5 \times 10^{6}}\)

= 0.15 m.