With a rise of temperature, the Young’s modulus :

Options

A. Increases
B. Decreases
C. Remains unchanged
D. Changes erratically

Explanation

To solve the question regarding how Young's modulus changes with a rise in temperature, we can follow these steps:

### Step 1: Understand Young's Modulus
Young's modulus (Y) is defined as the ratio of stress (force per unit area) to strain (deformation per unit length). The formula for Young's modulus is given by:

\[ Y = \frac{F \cdot L}{A \cdot \Delta L} \]

Where:
- \( F \) = Force applied
- \( L \) = Original length of the material
- \( A \) = Cross-sectional area
- \( \Delta L \) = Change in length

### Step 2: Analyze the Effect of Temperature on Length Change
The change in length (\( \Delta L \)) due to temperature change can be expressed as:

\[ \Delta L = L \cdot \alpha \cdot \Delta T \]

Where:
- \( \alpha \) = Coefficient of linear expansion
- \( \Delta T \) = Change in temperature

### Step 3: Substitute \(\Delta L\) into the Young's Modulus Formula
Substituting the expression for \(\Delta L\) into the Young's modulus formula gives:

\[ Y = \frac{F \cdot L}{A \cdot (L \cdot \alpha \cdot \Delta T)} \]

This simplifies to:

\[ Y = \frac{F}{A \cdot \alpha \cdot \Delta T} \]

### Step 4: Analyze the Relationship between Young's Modulus and Temperature
From the equation derived, we can see that as the temperature (\( \Delta T \)) increases, the denominator increases, which leads to a decrease in Young's modulus (Y). This indicates that:

- As temperature rises, Young's modulus decreases.

### Step 5: Understand the Practical Implications
Practically, as the temperature increases, materials tend to become softer and less rigid. This reduction in rigidity corresponds to a decrease in elasticity, which is what Young's modulus measures. Therefore, with an increase in temperature, the Young's modulus decreases.

### Conclusion
Thus, we conclude that with a rise in temperature, the Young's modulus decreases.

### Final Answer
The Young's modulus decreases with a rise in temperature.

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