Question

A rod of mass M and length L is hanging from ceiling. If the young modulus of rod is Y. Find elongation in rod due to its own weight.​

Answer 1

Answer:

Since the entire weight mg of the wire is concentrated at it at its centre of mass which lies at the geometrical centre

of the wire. So the effective original length of the wire is L2. According to Hooke's Law

Y=stressstrain

Y=mgA△LL2⇒△L=mgL2AY

Answer 2

Explanation:

Weight of the rod =mg

Area of cross section of the rod =A

Hence

Stress on the rod = mg

Let the change in length of the rod =L'

Original length of the rod =L

So strain = L'/L

We know that ,

Youngs modulus = stress/strain

Y= (mg/A)/(L' /L)

Y=mgL/AL'

L'=AY/mgL

Hence the change in length under its own weight will be AY/mgL