Error propagation in pendulum g calculation

Steps:

• Rearrange T=2π√(L/g) to g=4π²L/T²; relative uncertainty in g is δL/L + 2(δT/T).
• Calculate δL/L = 0.2/87 ≈ 0.0023 (0.23%).
• Calculate δT/T = 0.05/1.9 ≈ 0.0263 (2.63%); doubled is 5.26%.
• Add uncertainties: 0.23% + 5.26% ≈ 5.5%, rounds to 5%.

Why C is correct:

• The formula for relative error in g=constant×L/T² directly gives δg/g = δL/L + 2δT/T, yielding ~5%.

Why the others are wrong:

• A: Ignores dominant T uncertainty; only δL/L ≈0.2%, not total.
• B: Averages uncertainties instead of adding; underestimates T's doubled effect.
• D: Adds absolute errors without relative scaling or squaring T's role.

Final answer: C