Uncertainty propagation for g = 2s / t²

Steps:

• Relative uncertainty in g equals relative uncertainty in s plus relative uncertainty in t², since g ∝ s/t² and uncertainties add for multiplication/division.
• Percentage uncertainty in t² equals 2 times percentage uncertainty in t, from the power rule for uncertainties.
• Percentage uncertainty in t² = 2 × 2% = 4%.
• Total percentage uncertainty in g = 3% + 4% = 7%, closest to 8%.

Why C is correct:

• Maximum percentage uncertainty follows %Δg = %Δs + 2(%Δt) from differentiation of g = 2s/t², yielding 3% + 4% = 7%, matching 8% as the nearest option.

Why the others are wrong:

• A. 1%: Subtracts uncertainties, invalid for propagation in quotients.
• B. 5%: Uses root-sum-square √(3² + 4²) for random errors, not maximum uncertainty.
• D. 11%: Overcounts by misapplying powers, e.g., 3% + 2×4%.

Final answer: C