Taking long both the sides

$\log Y =\log 4 Fl -\log \pi D ^2 e$

Now, partially differentiating,

$\frac{\Delta Y }{ Y }=-\left(\frac{2 \Delta D }{ D }+\frac{\Delta e }{ e }\right)$

$\frac{\Delta Y }{ Y }=-\left(\frac{2 \times 0.01}{0.4}+\frac{0.05}{0.8}\right)$

$\frac{\Delta Y }{ Y }=-0.1125$

$\text { Also, } Y =\frac{ Fl }{ Ae }=\frac{9.8 \times 2}{\pi(0.2)^2 \times 0.8}=194.96 \times 10^9 \approx 2 \times 10^{11}$

$\Delta Y =- Y \times\left(\frac{2 \Delta r }{ r }+\frac{\Delta e }{ e }\right)$

$\Delta Y =0.225 \times 10^{11}$

$Y =(2 \pm 0.2) \times 10^{11} Nm ^{-2}$