If s is stress and Y is Young's modulus of material, the energy stored per unit volum is

Options

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

Answer

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

### Step-by-Step Solution:

1. **Understanding Energy Stored**: The energy (E) stored per unit volume in a material under stress can be expressed in terms of stress and strain. The formula for energy stored per unit volume is given by:
\[ E = \frac{1}{2} \times \text{stress} \times \text{strain} \]

2. **Substituting Stress**: We know that stress (s) is given in the problem. So we can rewrite the formula as:
\[ E = \frac{1}{2} \times s \times \text{strain} \]

3. **Relating Strain to Young's Modulus**: Young's modulus (Y) is defined as the ratio of stress to strain:
\[ Y = \frac{s}{\text{strain}} \]
From this, we can express strain in terms of stress and Young's modulus:
\[ \text{strain} = \frac{s}{Y} \]

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

5. **Simplifying the Expression**: This simplifies to:
\[ E = \frac{1}{2} \times \frac{s^2}{Y} \]

6. **Final Result**: Therefore, the energy stored per unit volume is given by:
\[ E = \frac{s^2}{2Y} \]

### Conclusion:
The energy stored per unit volume in terms of stress (s) and Young's modulus (Y) is:
\[ E = \frac{s^2}{2Y} \]