Properties Of Matter

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