The Young modulus E E\,E of a metal wire can be determined using the expression:
E=4FLπd2e E = \frac{4 F L}{\pi d^2 e} E=πd2e4FLwhere F F\,F is the applied tension force, L L\,L is the original length of the wire, d d\,d is the diameter of the wire, and e e\,e is the extension.
A student measures these quantities and estimates their percentage uncertainties as follows:
| Quantity | Percentage uncertainty |
|---|---|
| Tension force (FFF) | 1.2% |
| Original length (LLL) | 0.5% |
| Diameter (ddd) | 1.8% |
| Extension (eee) | 2.5% |
What is the percentage uncertainty in the calculated value of EEE?
2.8%2.8\%2.8%
6.0%6.0\%6.0%
7.8%7.8\%7.8%
9.6%9.6\%9.6%
