Question

A uniform rod of mass m, length l, area of cross section A and Young's modulus Y hangs from the ceiling. Its elongation under its own weight will be?

Answer 1

The change in length will be mgl/AY

Explanation:

Weight of the rod = mg

Area of cross section of the rod =A

Hence

Stress on the rod = mg/A

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'

or

l' = mgl/AY

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

Answer 2

Answer:

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