Young.s modulus of a wire is `2 xx 10^(11)N//m^(2)`. If a stress of 2 x 108 N/m2 is applied at the free end of a wire, find the strain in the wire.

Answer

To find the strain in the wire when a stress is applied, we can use the relationship defined by Young's modulus. The formula is given by:

\[ \text{Young's Modulus} (Y) = \frac{\text{Stress}}{\text{Strain}} \]

From this, we can rearrange the formula to find strain:

\[ \text{Strain} = \frac{\text{Stress}}{\text{Young's Modulus}} \]

### Step-by-Step Solution:

1. **Identify the given values**:
- Young's modulus \( Y = 2 \times 10^{11} \, \text{N/m}^2 \)
- Stress \( \sigma = 2 \times 10^{8} \, \text{N/m}^2 \)

2. **Substitute the values into the strain formula**:
\[ \text{Strain} = \frac{2 \times 10^{8} \, \text{N/m}^2}{2 \times 10^{11} \, \text{N/m}^2} \]

3. **Simplify the expression**:
- The \( 2 \) in the numerator and denominator cancels out:
\[ \text{Strain} = \frac{10^{8}}{10^{11}} \]

4. **Apply the laws of exponents**:
\[ \text{Strain} = 10^{8 - 11} = 10^{-3} \]

5. **Final result**:
\[ \text{Strain} = 1 \times 10^{-3} \]

### Conclusion:
The strain in the wire is \( 1 \times 10^{-3} \) (or \( 0.001 \)).