A wire is stretched by hanging a weight from its end and develops a longitudinal strain $σ_{1}$ , Y being the Young's modulus, elastic potential energy of the wire per unit volume can be expressed as:

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$\frac{Y σ_{l}}{2}$

$\frac{{Yσ}_{l}^{2}}{2}$

$\frac{3 {Yσ}_{l}^{2}}{2}$

$\frac{{Yσ}_{l}^{2}}{4}$

answer is B.

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Detailed Solution

Elastic potential energy per unit volume
$= \frac{1}{2} \times stress \times strain = \frac{1}{2} \times Y \times {(strain)}^{2} = \frac{1}{2} {Yσ}_{l}^{2}$

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