Mathematics in Physics

JEE Main level, single correct, medium

55 of 121

Question 55 of 121

Four persons measure the length of a rod as 20.00 cm,19.75 cm,17.01 cm20.00 \mathrm{~cm}, 19.75 \mathrm{~cm}, 17.01 \mathrm{~cm} and 18.25 cm. The relative error in the measurement of average length of the rod is :

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Answer: (B) 0.06

Mean =20.00+19.75+17.01+18.254=75.014=18.7525= \frac{20.00+19.75+17.01+18.25}{4} = \frac{75.01}{4} = 18.7525 cm.
Absolute errors: ∣20.00−18.7525∣=1.2475|20.00-18.7525|=1.2475, ∣19.75−18.7525∣=0.9975|19.75-18.7525|=0.9975, ∣17.01−18.7525∣=1.7425|17.01-18.7525|=1.7425, ∣18.25−18.7525∣=0.5025|18.25-18.7525|=0.5025.
Mean absolute error =1.2475+0.9975+1.7425+0.50254=4.494=1.1225= \frac{1.2475+0.9975+1.7425+0.5025}{4} = \frac{4.49}{4} = 1.1225.
Relative error =1.122518.7525≈0.06= \frac{1.1225}{18.7525} \approx 0.06.

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