Acceleration due to gravity is determined using g = 4π²L/T². The maximum percentage error in L is 1%. Time t for N = 50 oscillations is measured with maximum percentage error 0.5%. Assuming N is exact, the maximum percentage error in g is:
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Question

Acceleration due to gravity is determined using g = 4π²L/T². The maximum percentage error in L is 1%. Time t for N = 50 oscillations is measured with maximum percentage error 0.5%. Assuming N is exact, the maximum percentage error in g is:

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G1 Physics · Accepted Answer

T = t/N. Since N is exact, ΔT/T = Δt/t = 0.5%. Now g ∝ LT⁻². Therefore Δg/g = ΔL/L + 2ΔT/T = 1% + 2(0.5%) = 2%. Hence the maximum percentage error in g is 2%.