A student determines g from g=4π²ℓ/T² with ℓ≈1 m. Length error is Δℓ, time n oscillations is measured with stopwatch least count ΔT and human error 0.1 s. Which data set gives the most accurate g?
Options

Question

A student determines g from g=4π²ℓ/T² with ℓ≈1 m. Length error is Δℓ, time n oscillations is measured with stopwatch least count ΔT and human error 0.1 s. Which data set gives the most accurate g?

Options

G1 Physics · Accepted Answer

For g=4π²ℓ/T², fractional error is Δℓ/ℓ +2ΔT/T. Accuracy improves with smaller length error, smaller timing error, more oscillations and small amplitude. Dataset D minimizes all these contributions. Correct answer: D.