In an experiment to determine the Young's modulus of wire of a length exactly 1 m, the extension in the length of the wire is measured as 0.4 mm with…

In an experiment to determine the Young's modulus of wire of a length exactly $\displaystyle 1$ m , the extension in the length of the wire is measured as $\displaystyle 0.4$ mm with an uncertainty of ± $\displaystyle 0.02$ mm when a load of $\displaystyle 1$ kg is applied. The diameter of the wire is measured as $\displaystyle 0.4$ mm with an uncertainty of $\displaystyle \pm 0.01 \mathrm{~mm}$. The error in the measurement of Young's modulus $\displaystyle (\Delta \mathrm{Y})$ is found to be $\displaystyle x \times 10^{10} \mathrm{Nm}^{-2}$. The value of $\displaystyle x$ is \_\_\_\_. (take $\displaystyle \mathrm{g}=10 \mathrm{~ms}^{-2}$ )