AS Daily A Level Physics question
In a required practical to estimate the density of a short cylindrical metal rod, a student measures mass m with a digital balance (±0.01 g), length L with a steel ruler (±0.5 mm), and diameter d with a micrometer (±0.01 mm). The rod is about L = 50 mm and d = 6 mm, and the micrometer readings vary noticeably around the circumference (slight ovality). Density is calculated from m and the cylindrical volume. Without changing the overall method, which single change would most reduce the percentage uncertainty in the final density?
Answer
The correct answer is C.
Correct: C — Measure d at several angles and positions along the rod (at least eight readings) and average the values. Diameter enters the cylindrical volume as d squared, so its percentage uncertainty is effectively doubled in the density; since d also shows the largest scatter from ovality, taking many readings and averaging most directly reduces the dominant contribution. A Reducing the balance resolution further targets a contribution that is already small compared with length and especially diameter, so it has little effect on the overall percentage uncertainty. B Making L larger does reduce its percentage uncertainty, but L contributes only linearly while the diameter term is both larger (due to ovality) and doubled in the density calculation, so this change is not the most effective. C This addresses the largest and most strongly weighted uncertainty (d), and averaging reduces random variation from ovality and measurement scatter. D Averaging many mass readings mainly reduces random scatter, but the balance already gives highly repeatable readings and the resolution limit remains; mass is not the dominant source here.