Four persons measure the length of a rod as 20.00 cm, 19.75 cm, 17.01 cm and 18.25 cm. The relative error in the measurement of average length of the rod is :
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Question

Four persons measure the length of a rod as 20.00 cm, 19.75 cm, 17.01 cm and 18.25 cm. The relative error in the measurement of average length of the rod is :

G1 Physics · Accepted Answer

The mean measured length is L(mean) = (20.00 + 19.75 + 17.01 + 18.25)/4 = 75.01/4 = 18.7525 cm ≈ 18.75 cm. Absolute deviations from the mean are approximately |20.00 - 18.75| = 1.25 cm, |19.75 - 18.75| = 1.00 cm, |17.01 - 18.75| = 1.74 cm, |18.25 - 18.75| = 0.50 cm. Mean absolute error: ΔL(mean) = (1.25 + 1.00 + 1.74 + 0.50)/4 = 4.49/4 ≈ 1.12 cm. Therefore the relative error is ΔL(mean)/L(mean) = 1.12/18.75 ≈ 0.06. Correct option: C.