\(\Delta L =0.4 \times 10^{-3} m\)

\(m =1\,kg\)

\(d =0.4 \times 10^{-3}\,m\)

\(\frac{ F }{ A }= Y \frac{\Delta L }{ L }\)

\(Y =\frac{ FL }{ A \Delta L }=\frac{( mg ) \cdot(1)}{\left(\frac{\pi d ^{2}}{4}\right) 0.4 \times 10^{-3}}\)

\(\Rightarrow \frac{10 \times 4}{\pi\left(0.4 \times 10^{-3}\right)^{2} \times 0.4 \times 10^{-3}}\)

\(Y =\frac{40}{\pi\left(0.4 \times 10^{-3}\right)^{3}}\)

\(Y =\frac{40 \times 7}{22 \times 64 \times 10^{-3} \times 10^{-9}}\)

\(Y =0.199 \times 10^{-12} N / m ^{2}\)

\(\frac{\Delta Y }{ Y }=\frac{\Delta F }{ F }+\frac{\Delta L }{ L }+\frac{\Delta A }{ A }+\frac{\Delta(\Delta L )}{(\Delta L )}\)

\(=\frac{0.02}{0.4}+2 \frac{\Delta d }{ d }=\frac{0.2}{4}+2 \times \frac{0.01}{0.4}\)

\(=\frac{0.1}{2}+\frac{0.1}{2}=0.1\)

\(\Rightarrow \Delta Y =0.1 \times Y\)

\(=0.199 \times 10^{11}=1.99 \times 10^{10}\)