The Young modulus of the material in a wire is to be determined. The Young modulus $E$ is given by the equation $E = \frac{4Fl}{\pi d^{2} x}$. A known force is applied to stretch the wire and the following measurements are taken. Which measurement contributes the greatest effect to the uncertainty in the calculated Young modulus?
- Alength of wire before force applied, $l = 2.043 \pm 0.002\,\text{m}$
- Bdiameter of wire, $d = 0.54 \pm 0.02\,\text{mm}$
- Cforce applied, $F = 19.62 \pm 0.01\,\text{N}$
- Dextension of wire with force applied, $x = 5.2 \pm 0.2\,\text{mm}$