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A wire is stretched so that the stress in it is S and the Young’s modulus of its material is Y. What is the elastic energy stored per unit volume of the wire?

1. S²/2Y
2. 2S²Y
3. S/2Y
4. 2Y/S²

Correct answer: S²/2Y

Solution

The elastic energy stored per unit volume in a material under stress can be derived from the relationship between stress and strain, where the energy density is given by the formula U = (1/2) * stress * strain. Since strain can be expressed as stress divided by Young's modulus (strain = S/Y), substituting this into the energy density formula leads to U = (1/2) * S * (S/Y) = S²/(2Y).

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