A thick rope of density `rho` and length `L` is hung from a rigid support. The increase in length of the rope due to its own weight is (`Y` is the Young's modulus)

Explanation

Let A be the area of corsssection of the rope. Weight of the rope, `F=AL rho g`. It will be acting at the centre of gravity of the rope which lies at a distance `L//2` form the rigid support. Therefore,
`Y= ("normal stress")/("longitudinal stress") = (AL roh g//A)/(Delta L//(L//2))`
or `Delta L = (L^(2)rho g)/(2Y)`.