Question

A thick rubber rope of length L,density p and Youngs modulus Y is hung from the ceiling of a room What is the increase in its length due to its own weight?​

Answer 1

Answer:

Take a small section δy at distance y from top as shown in figure. Let area of rope be A

Stress due to this section = ρAgδy/A=ρdδy

Strain on section y = δl/y

Using Stress = Y \times Strain

=> ρgδy=Y×

y

δl

=>Δl=

y

ρg

∫

0

L

yδy

=> Δl=

2Y

ρgL

2

Answer.

2Y

ρgL

2