Question

Density of rubber is d.A thick rubber cord of length L and cross section area A undergoes elongation under its own weight on suspending it. This elongation is proportional to

Answer 1

Elongation is directly proportional to dL²

Given-

• Density of rubber = d
• Length of rubber cord = L
• Cross section area of rubber cord = A

A thin section dx is taken in the rod.

mg is the force acting in the thin section dx in downward direction.

Suppose elongation in the thin section is dy.

We know that Young's modulus (Y) is = mg/A/dy/dx

Y = mg × dx / A × dy

dy = mg × dx / A × Y

By putting the value of mg and integrating it we get

We know that mass is equals to volume × density

m = x A d

dy = x A d dx / AY

∫dy = d/Y ∫x. dx ( limits of dy is from 0 to X and limits of dx is from 0 to L)

X = d/Y (L²/2)

X = dL²/2Y

X is the elongation

Answer 2

Answer:

Increment in length l=2YdL2g

∴l ∝ dL2