Question

What will be the elastic potential energy per unit volume when a metal wire is suspended along with a suspending weight on it?

(a) Y^2α

(b) \(\frac{1}{2}\) Yα^2

(c) 4Yα

(d) 8Y^2α^2

I had been asked this question by my college director while I was bunking the class.

I would like to ask this question from Strength of Materials topic in chapter Strength of Materials and Construction Materials of Farm Machinery

Answer 1

The correct choice is (b) \(\frac{1}{2}\) Yα^2

Easiest explanation: The elastic potential energy per unit volume,  u = \(\frac{1}{2}\) *stress*strain

Y = \(\frac{Stress}{Strain} \)

Stress = Y * Strain = Y*α

U = \(\frac{1}{2}\)*Y*α*α = \(\frac{1}{2}\)*Y*α^2