AS Daily A Level Physics question
In a lab test to determine a metal wire’s stiffness, a student measures between two marks 2.00 m apart. The wire’s diameter is 0.50 mm with an uncertainty of ±0.01 mm (from a micrometer). Under the maximum load, the extension between the marks is 1.0 mm with an uncertainty of ±0.1 mm (from a ruler). The hanging masses used to apply the load are calibrated so their uncertainty can be ignored. Which single measurement contributes the largest percentage uncertainty to the calculated Young modulus?
Answer
The correct answer is D.
Correct: D — The extension measurement of the wire under load. The percentage uncertainty in extension is about 0.1/1.0 = 10%, which dominates the calculation. A The diameter has about 0.01/0.50 = 2% uncertainty, and because area depends on diameter squared this contributes roughly 4% to the modulus — smaller than 10%. B The original length has about 1 mm out of 2000 mm ≈ 0.05% uncertainty, negligible compared with 10%. C The applied force uncertainty is stated as negligible from the calibrated masses, so it does not dominate. D This is correct because the small absolute extension makes its relative (percentage) uncertainty the largest.