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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Correct Answer

(C) 0.06

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Detailed explanation

\(\ell_{\text {mean }}=\frac{\ell_1+\ell_2+\ell_3+\ell_4}{4}\)
\(\ell_{\text {mean }}=\frac{20.00+19.75+17.01+18.25}{4}\)
\(=18.75\)
\(\Delta \ell_{\text {mean }}=\frac{\left|\Delta \ell_1\right|+\left|\Delta \ell_2\right|+\left|\Delta \ell_3\right|+\left|\Delta \ell_4\right|}{4}\)
\(=\frac{1.25+1+1.74+0.5}{4}=1.12\)
So, relative error
\(=\frac{\Delta \ell_{\text {mean }}}{\ell_{\text {mean }}}=\frac{1.12}{18.75}=0.06\)

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