An experiment determines g from g = 4π²(L₁ + L₂)/T². Measurements are L₁ = (40.0 ± 0.2) cm, L₂ = (60.0 ± 0.3) cm and T = (2.00 ± 0.01) s. The maximum percentage error in g is:
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An experiment determines g from g = 4π²(L₁ + L₂)/T². Measurements are L₁ = (40.0 ± 0.2) cm, L₂ = (60.0 ± 0.3) cm and T = (2.00 ± 0.01) s. The maximum percentage error in g is:

G1 Physics · Accepted Answer

First, L = L₁ + L₂ = 100.0 cm. For addition, absolute errors add: ΔL = 0.2 + 0.3 = 0.5 cm. Thus percentage error in L = (0.5/100.0)×100 = 0.5%. Percentage error in T = (0.01/2.00)×100 = 0.5%. Since g ∝ LT⁻², maximum percentage error = 0.5% + 2(0.5%) = 1.5%.