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: [2026]

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Solution

Q.
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: [2026]

1 0.08

2 0.18

3 0.24

4 0.06

Ans.
(4)

$ℓ_{mean} = \frac{ℓ_{1} + ℓ_{2} + ℓ_{3} + ℓ_{4}}{4}$

$ℓ_{mean} = \frac{20.00 + 19.75 + 17.01 + 18.25}{4}$

$= 18.75$

$Δ ℓ_{mean} = \frac{| Δ ℓ_{1} | + | Δ ℓ_{2} | + | Δ ℓ_{3} | + | Δ ℓ_{4} |}{4}$

$= \frac{1.25 + 1 + 1.74 + 0.5}{4} = 1.12$

$So, relative error$

$= \frac{Δ ℓ_{mean}}{ℓ_{mean}}$ $= \frac{1.12}{18.75}$ $= 0.06$

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