On applying a stress of 20 x 10⁸ N / m² the length of a perfectly elastic wire is doubled. Its Young’s modulus will be

The correct option is 20 x 10⁸ N / m².

To find the Young's modulus of the wire, we use the relationship between stress, strain, and Young's modulus.

Let the initial length of the perfectly elastic wire be $L$.

According to the problem, the length of the wire is doubled under the applied stress. Therefore, the final length of the wire is $2L$.

The change in length ($\Delta L$) is calculated as:
$\Delta L=2L-L=L$

The longitudinal strain is the ratio of the change in length to the original length:
$\text{Strain}=\frac{\Delta L}{L}=\frac{L}{L}=1$

Young's modulus ($Y$) is defined as the ratio of tensile stress to longitudinal strain:
$Y=\frac{\text{Stress}}{\text{Strain}}$

Given that the applied stress is 20 x 10⁸ N/m², we substitute the values into the formula:
$Y=\frac{20\times {10}^8{\text{N/m}}^2}{1}=20\times {10}^8{\text{N/m}}^2$

Thus, the Young's modulus of the wire is 20 x 10⁸ N/m² (which matches the option 20 x 10⁸ N / m²).