The ratio of tensile stress to the longitudinal strain is defined as

Options

A. Bulk modulus
B. Young's modulus
C. Shear modulus
D. Compressibility

Explanation

To solve the question regarding the ratio of tensile stress to longitudinal strain, we can follow these steps:

### Step-by-Step Solution:

1. **Define Tensile Stress**:
- Tensile stress (σ) is defined as the force (F) applied per unit area (A) over which the force is distributed.
- Mathematically, it is expressed as:
\[ \sigma = \frac{F}{A} \]

2. **Define Longitudinal Strain**:
- Longitudinal strain (ε), also known as tensile strain, is defined as the change in length (ΔL) divided by the original length (L) of the material.
- Mathematically, it is expressed as:
\[ \epsilon = \frac{\Delta L}{L} \]

3. **Formulate the Ratio**:
- The ratio of tensile stress to longitudinal strain is given by:
\[ \frac{\sigma}{\epsilon} \]

4. **Substitute the Definitions**:
- Substitute the expressions for tensile stress and longitudinal strain into the ratio:
\[ \frac{\sigma}{\epsilon} = \frac{\frac{F}{A}}{\frac{\Delta L}{L}} \]

5. **Simplify the Expression**:
- To simplify, we can multiply by the reciprocal of the strain:
\[ \frac{\sigma}{\epsilon} = \frac{F}{A} \cdot \frac{L}{\Delta L} = \frac{F \cdot L}{A \cdot \Delta L} \]

6. **Identify the Result**:
- This ratio is defined as Young's modulus (E), which is a measure of the stiffness of a solid material.
- Therefore, we conclude:
\[ \frac{\sigma}{\epsilon} = E \]

### Final Answer:
The ratio of tensile stress to longitudinal strain is defined as **Young's modulus**.

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