The temperature of a wire is doubled. The Young's modulus of elasticity

Options

A. also double
B. become four times
C. remain same
D. decrease.

Explanation

To solve the problem regarding the effect of doubling the temperature on the Young's modulus of elasticity, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Young's Modulus**:
Young's modulus (Y) is defined as the ratio of stress (force per unit area) to strain (deformation per unit length) in a material. Mathematically, it is expressed as:
\[ Y = \frac{\text{Stress}}{\text{Strain}} = \frac{F/A}{\Delta L / L} \]
where \( F \) is the force applied, \( A \) is the cross-sectional area, \( \Delta L \) is the change in length, and \( L \) is the original length.

2. **Effect of Temperature on Length**:
When the temperature of a wire increases, it expands. The change in length (\( \Delta L \)) due to temperature change can be expressed as:
\[ \Delta L = \alpha L \Delta T \]
where \( \alpha \) is the coefficient of linear expansion and \( \Delta T \) is the change in temperature.

3. **Relating Strain to Temperature**:
The strain (\( \frac{\Delta L}{L} \)) can be rewritten using the equation for change in length:
\[ \frac{\Delta L}{L} = \alpha \Delta T \]

4. **Substituting into Young's Modulus**:
Substituting the expression for strain into the equation for Young's modulus gives:
\[ Y = \frac{F/A}{\alpha \Delta T} \]

5. **Analyzing the Effect of Doubling Temperature**:
If the initial temperature is \( T_1 \) and it is doubled to \( 2T_1 \), the change in temperature (\( \Delta T \)) will also increase. Since Young's modulus is inversely proportional to the temperature change (as seen from the equation \( Y \propto \frac{1}{\Delta T} \)), we can conclude that:
- As temperature increases, Young's modulus decreases.

6. **Conclusion**:
Therefore, when the temperature is doubled, the Young's modulus of elasticity decreases.

### Final Answer:
The Young's modulus of elasticity decreases when the temperature of the wire is doubled. The correct option is **D**.