A metallic wire is stretched by suspending a weight of it. If `alpha` is the longitudinal strain and `Y` is its Young's modulus of elasticity, then slow that the elastic potential energy per unit volume is given by `1/2Yalpha^(2)`.

Explanation

To prove that the elastic potential energy per unit volume (U) of a metallic wire stretched by a weight is given by the formula:

\[ U = \frac{1}{2} Y \alpha^2 \]

where \( \alpha \) is the longitudinal strain and \( Y \) is the Young's modulus of elasticity, we can follow these steps:

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