According to Hooke's law of elasticity, if stress is increased, the ratio of stress to strain

Options

A. decreases
B. increases
C. becomes zero
D. remains constant

Explanation

To solve the question regarding Hooke's law of elasticity and the relationship between stress and strain, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Hooke's Law**: Hooke's law states that the stress applied to a material is directly proportional to the strain produced in that material, as long as the material is within its elastic limit. Mathematically, this can be expressed as:
\[ \text{Stress} \propto \text{Strain} \]

2. **Define Stress and Strain**:
- **Stress** (\( \sigma \)) is defined as the force (\( F \)) applied per unit area (\( A \)):
\[ \sigma = \frac{F}{A} \]
- **Strain** (\( \epsilon \)) is defined as the change in length (\( \Delta L \)) divided by the original length (\( L_0 \)):
\[ \epsilon = \frac{\Delta L}{L_0} \]

3. **Introduce Young's Modulus**: Young's modulus (\( E \)) is defined as the ratio of stress to strain:
\[ E = \frac{\sigma}{\epsilon} \]
According to Hooke's law, this ratio remains constant for a given material as long as the material is not deformed beyond its elastic limit.

4. **Analyze the Effect of Increasing Stress**: If we increase the stress applied to the material, the strain will also increase proportionally. However, the ratio of stress to strain (which equals Young's modulus) remains constant:
\[ \text{If } \sigma \text{ increases, then } \epsilon \text{ increases such that } \frac{\sigma}{\epsilon} = E \text{ remains constant.} \]

5. **Conclusion**: Therefore, according to Hooke's law, if stress is increased, the ratio of stress to strain remains constant and is equal to Young's modulus.

### Final Answer:
The ratio of stress to strain remains constant according to Hooke's law of elasticity, and this ratio is equal to Young's modulus.

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