On applying a stress of `xN//m^(2)`, the length of wire of some material gets doubled. Value of Young's modulus for the material of wire in `N//m^(2)`, is (assume Hooke's law to be valid and go for approx. results)

Options

A. `x`
B. `2x`
C. `x/2`
D. Insufficient information

Explanation

To solve the problem, we need to find the Young's modulus (Y) of a material given that a wire doubles its length when a stress of \( x \, \text{N/m}^2 \) is applied. We will use the relationship defined by Hooke's law, which states that Young's modulus is the ratio of stress to strain.

### Step-by-Step Solution:

1. **Understand the Definitions**:
- **Stress** (\( \sigma \)): It is defined as the force applied per unit area. In this case, it is given as \( x \, \text{N/m}^2 \).
- **Strain** (\( \epsilon \)): It is defined as the change in length divided by the original length.

2. **Calculate the Change in Length**:
- Let the original length of the wire be \( l \).
- The final length after applying the stress is \( 2l \) (since it doubles).
- The change in length (\( \Delta L \)) is given by:
\[ \Delta L = \text{Final Length} - \text{Original Length} = 2l - l = l \]

3. **Calculate the Strain**:
- Strain (\( \epsilon \)) can be calculated as:
\[ \epsilon = \frac{\Delta L}{l} = \frac{l}{l} = 1 \]

4. **Calculate the Young's Modulus**:
- Young's modulus (\( Y \)) is defined as:
\[ Y = \frac{\text{Stress}}{\text{Strain}} = \frac{\sigma}{\epsilon} \]
- Substituting the values we have:
\[ Y = \frac{x}{1} = x \, \text{N/m}^2 \]

5. **Final Result**:
- Therefore, the value of Young's modulus for the material of the wire is:
\[ Y = x \, \text{N/m}^2 \]

### Summary:
The Young's modulus of the material of the wire is \( x \, \text{N/m}^2 \).