AS Daily A Level Physics question
In a lab determination of Young modulus using a steel wire, you plot force against extension measured with a ruler that reads to 0.5 mm. The main limitation is that the extensions are small compared with this reading resolution. You must keep the same maximum load and stay within the elastic region. Which single change will most reduce the percentage uncertainty in the gradient of the force–extension graph?
Answer
The correct answer is D.
Correct: D — Use a longer, thinner wire of the same material (still elastic). For a given force the extension is proportional to length and inversely proportional to cross-sectional area, so making the wire longer and thinner increases the extension measured for each load and reduces the percentage effect of a fixed 0.5 mm reading step. A … Shortening the wire reduces extension for each load, increasing the percentage uncertainty from the same resolution. B … Averaging repeats cannot overcome a fixed reading resolution when values are quantised to 0.5 mm; it reduces random scatter but not the dominant resolution limit here. C … Starting from zero load without a small preload leaves kinks/slack, introducing nonlinearity and bias; it does not increase the measurable extension per load within the elastic region. D … Lengthening and thinning (within elastic limits) increases the signal relative to the fixed reading step, giving the largest reduction in percentage uncertainty.