JEE Main 2022 · 26 Jul · Shift 1, Physics question 53

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 an uncertainty of ± 0.02 mm when a load of 1 kg is applied. The diameter of the wire is measured as 0.4 mm with an uncertainty of ± 0.01 mm. The error in the measurement of Young's modulus ($\Delta Y$) is found to be $x\times10^{10}$ Nm$^{-2}$. The value of $x$ is ______.

(take $g=10$ ms$^{-2}$)