Question

The diameter of a given wire is measured by a screw gauze. The three measurements of the diameter give the reading in $cm$ as $0.036, 0.035$ and $0.037$. What is the percentage error of the measurement?

• A. 1.8%
• B. 2.8%
• C. 3.2%
• D. 4.6%

Answer 1

Answer: (A)

Mean measurement of wire $=\frac{0.036+0.035+0.037}{3}=0.036 \,cm$
Taking $0,036\, cm$ as the true value, the absolute errors (true value - measured value) in the three readings taken are
$0.036-0.036=0.036-0.035=0.001 cm 0.036-0.037=-0.001\, cm$
The (maximum) mean absolute error is
$\delta d_{\max }=\frac{0+001+0.001}{3}=0.00066 \,cm$
The percentage error is
$=\frac{0.00066}{0.036} \times 100=1.8 \%$