A2 Daily A Level Physics question
In a required practical to determine g using a simple pendulum, a student measures the length L with a 2% uncertainty and the period T with a 1% uncertainty (from timing many swings). Using that g is proportional to L/T^2, what is the percentage uncertainty in g?
Answer
The correct answer is C.
Correct: C — Approximately 4%. Because g ∝ L/T^2, fractional uncertainties add with powers: Δg/g ≈ ΔL/L + 2(ΔT/T) = 2% + 2×1% = 4%. A adds 2% and 1% but ignores the squared dependence on T. B assumes only the length uncertainty contributes, which is wrong because T appears in the denominator squared. C follows the correct propagation rule for a product and a squared term. D overestimates by effectively double-counting or incorrectly squaring both uncertainties.