If 'S' is stress and 'Y' is young's modulus of material of a wire, the energy stored in the wire per unit volume is

Options

A. `S/(2Y)`
B. `(2Y)/S^2`
C. `S^2/(2Y)`
D. `2 S^2 Y`

Answer

To find the energy stored in a wire per unit volume when given stress (S) and Young's modulus (Y), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept**:
The energy stored in a material due to deformation can be expressed in terms of stress and strain. The formula for energy stored per unit volume (U) is given by:
\[ U = \frac{1}{2} \times \text{stress} \times \text{strain} \]

2. **Expressing Strain in Terms of Stress and Young's Modulus**:
We know that stress (S) and strain (ε) are related through Young's modulus (Y) by the equation:
\[ \text{strain} = \frac{\text{stress}}{Y} \quad \Rightarrow \quad \epsilon = \frac{S}{Y} \]

3. **Substituting Strain into the Energy Formula**:
Now, we can substitute the expression for strain into the energy formula:
\[ U = \frac{1}{2} \times S \times \left(\frac{S}{Y}\right) \]

4. **Simplifying the Expression**:
This simplifies to:
\[ U = \frac{1}{2} \times \frac{S^2}{Y} \]

5. **Final Result**:
Thus, the energy stored in the wire per unit volume is:
\[ U = \frac{S^2}{2Y} \]

### Conclusion:
The correct expression for the energy stored in the wire per unit volume is \( \frac{S^2}{2Y} \).