d

To determine the elastic energy stored in a wire under tension, we can use the concepts of stress, strain, and Young's modulus (Y).
Step 1: Understand the relationships:
Stress ($ au$) is defined as force per unit area, and strain ($ ext{ε}$) is the deformation per unit length. Young's modulus (Y) is defined as the ratio of stress to strain:
$$ Y = \frac{\text{Stress}}{\text{Strain}} = \frac{\tau}{\text{ε}} $$
Step 2: Elastic energy (U) stored in a wire can be expressed in terms of stress and strain:
$$ U = \frac{1}{2} \times \text{Stress} \times \text{Strain} \times V $$
where V is the volume of the wire.
Step 3: Replacing Stress with Y × Strain from the definition of Y, we get:
$$ U = \frac{1}{2} \times Y \times \text{Strain}^2 \times V $$
Thus, the correct answer which combines all these factors appropriately is option (d), which contains the term $rac{1}{2}Y \times \text{Stress} \times \text{Strain} \times V$. Hence, the correct answer is option d.