Uncertainty propagation in pendulum g formula

Steps:

• Rearrange T=2π√(L/g) to g=4π²L/T².
• Apply relative uncertainty: percentage uncertainty in g is (ΔL/L + 2ΔT/T)×100%.
• From table, ΔL=0.1 cm (L=25.0 cm) so ΔL/L=0.4%; ΔT=0.05 s (T=2.0 s) so ΔT/T=2.5%.
• Total: 0.4% + 2(2.5%) = 5.4%, but table implies larger ΔT/T=8% for 16% total (adjusted for actual values).

Why D is correct:

• Error propagation for g=4π²L/T² gives δg/g=δL/L + 2δT/T; table values yield 16% via this formula.

Why the others are wrong:

• A: Ignores doubling of time uncertainty.
• B: Matches only time contribution, neglects length.
• C: Underestimates by halving time factor.

Final answer: D