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

Options

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

Explanation

To solve the problem regarding Hooke's law of elasticity, we will follow these steps:

### Step 1: Understand Hooke's Law
Hooke's Law states that the stress applied to a material is directly proportional to the strain produced, as long as the material's elastic limit is not exceeded. This relationship can be mathematically expressed as:
\[ \text{Stress} \propto \text{Strain} \]

### Step 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 (\( L_0 \)):
\[ \epsilon = \frac{\Delta L}{L_0} \]

### Step 3: Introduce Young's Modulus
Young's modulus (\( E \)) is a measure of the stiffness of a material and is defined as the ratio of stress to strain:
\[ E = \frac{\sigma}{\epsilon} \]

### Step 4: Analyze the Effect of Increasing Stress
According to Hooke's law, if we increase the stress on a material, the strain will also increase proportionally, as long as we remain within the elastic limit of the material. Thus, we can express this relationship as:
\[ \sigma = E \cdot \epsilon \]

### Step 5: Determine the Ratio of Stress to Strain
From the definition of Young's modulus, we can rearrange the equation to find the ratio of stress to strain:
\[ \frac{\sigma}{\epsilon} = E \]

### Step 6: Conclusion
Since Young's modulus (\( E \)) is a constant for a given material, the ratio of stress to strain remains constant even if the stress is increased, as long as the material is within its elastic limit.

Thus, the answer to the question is that the ratio of stress to strain remains constant.

### Final Answer:
The ratio of stress to strain remains constant according to Hooke's law of elasticity.

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