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
1)
2) pgl/Y
pgl/Y
4) pgl/Y
1) pgl /Y
3)
11​

Answer 1

Answer:

Correct option is

B

2Y

1

ρL

2

g

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