Young's modulus of elasticity is the ratio of

Options

A. Hydraulic stress and hydraulic strain
B. Shearing stress and shearing strain
C. Tensile stress and longitudinal strain
D. Bulk stress and longitudinal strain

Answer

To solve the question regarding Young's modulus of elasticity, we need to understand the definitions and relationships between stress, strain, and the different types of moduli.

### Step-by-Step Solution:

1. **Understanding Young's Modulus**:
- Young's modulus (E) is a measure of the stiffness of a solid material. It quantifies the relationship between stress (force per unit area) and strain (deformation) in a material in the linear elastic region of the stress-strain curve.

2. **Defining Stress and Strain**:
- **Stress** is defined as the force (F) applied per unit area (A):
\[ \text{Stress} = \frac{F}{A} \]
- **Strain** is defined as the change in length (ΔL) divided by the original length (L):
\[ \text{Strain} = \frac{\Delta L}{L} \]

3. **Relationship of Young's Modulus**:
- Young's modulus is defined mathematically as:
\[ E = \frac{\text{Tensile Stress}}{\text{Longitudinal Strain}} = \frac{\frac{F}{A}}{\frac{\Delta L}{L}} \]

4. **Identifying the Correct Ratio**:
- From the definition, we can see that Young's modulus is specifically the ratio of **tensile stress** to **longitudinal strain**.
- Therefore, the correct answer to the question is that Young's modulus of elasticity is the ratio of tensile stress to longitudinal strain.

5. **Eliminating Incorrect Options**:
- The other options mentioned (hydraulic stress and strain, shearing stress and strain, bulk stress and strain) do not relate to Young's modulus:
- Hydraulic stress and strain relate to fluids.
- Shearing stress and strain relate to the modulus of rigidity (shear modulus).
- Bulk stress and strain relate to the bulk modulus.

### Conclusion:
Thus, the correct answer is that Young's modulus of elasticity is the ratio of **tensile stress to longitudinal strain**.