`[J. m^(-3)]` may be the unit of

Options

A. Strain energy density
B. Modulus of Elasticity
C. Both a & b
D. Strain energy

Answer

To determine what the unit `[J. m^(-3)]` may represent, we can analyze the options provided and relate them to the definitions of strain energy density, modulus of elasticity, and strain energy.

### Step-by-Step Solution:

1. **Understanding the Unit**:
The unit `[J. m^(-3)]` can be interpreted as joules per cubic meter (J/m³). This indicates a quantity that is measured in energy (joules) divided by volume (cubic meters).

2. **Strain Energy Density**:
- Strain energy density is defined as the energy stored in a material per unit volume due to deformation.
- The formula for strain energy density can be expressed as:
\[ \text{Strain Energy Density} = \frac{\text{Energy}}{\text{Volume}} \]
- The unit of energy is joules (J), and the unit of volume is cubic meters (m³).
- Therefore, the unit of strain energy density is:
\[ \text{Unit} = \frac{J}{m^3} = J \cdot m^{-3} \]

3. **Modulus of Elasticity**:
- The modulus of elasticity is defined as the ratio of stress (force per unit area) to strain (dimensionless).
- Stress is measured in pascals (Pa), where \(1 \, \text{Pa} = 1 \, \text{N/m}^2\).
- Therefore, the modulus of elasticity can be expressed as:
\[ \text{Modulus of Elasticity} = \frac{\text{Force}}{\text{Area}} = \frac{\text{N}}{m^2} \]
- Since \(1 \, \text{N} = 1 \, \text{J/m}\), we can rewrite the modulus of elasticity as:
\[ \text{Modulus of Elasticity} = \frac{J/m}{m^2} = \frac{J}{m^3} = J \cdot m^{-3} \]

4. **Strain Energy**:
- Strain energy is simply the total energy stored in the material due to deformation, which is measured in joules (J).
- It does not have a unit of J/m³ but rather just J.

5. **Conclusion**:
- From the analysis, both strain energy density and modulus of elasticity have the unit of \(J/m^3\).
- Therefore, the correct answer to the question is that `[J. m^(-3)]` may be the unit of both strain energy density and modulus of elasticity.

### Final Answer:
The unit `[J. m^(-3)]` may be the unit of:
- **Strain Energy Density**
- **Modulus of Elasticity**
- **Both A and B**

Thus, the correct option is **C: Both A and B**.