Question

A thick rope of density p and length 1 is hung from a rigid support. The
young's modulus of the material of rope is Y. The increase in length of
the rope due to its own weight is
​

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

 

​

Explanation: