2023 Units and MeasurementsCombination of Errors Medium Question 14 of 53 in Units and Measurements

A metal wire has mass $(0.4 \pm 0.002)$ g, radius $(0.3 \pm 0.001)$ mm and length $(5 \pm 0.02)$ cm. The maximum possible percentage error in the measurement of density will nearly be :

A 1.4%
B 1.2%
C 1.3%
D 1.6%

The answer is D.

Solution

Maximum error in $\rho=\frac{m}{\pi r^2 l}$ adds $\frac{\Delta m}{m}+\frac{2\Delta r}{r}+\frac{\Delta l}{l}\approx1.6\%$.

$m=\rho\pi r^2 l \Rightarrow \rho=\frac{m}{\pi r^2 l}$ $\frac{\Delta\rho}{\rho}=\frac{\Delta m}{m}+\frac{2\Delta r}{r}+\frac{\Delta l}{l}$ $\frac{\Delta\rho}{\rho}\times100=\frac{0.002}{0.4}\times100+\frac{2\times0.001}{0.3}\times100+\frac{0.02}{5}\times100$ $=\frac{0.2}{0.4}+\frac{0.2}{0.3}+\frac{2}{5}=0.5+0.67+0.4=1.57\approx1.6\%$

Concept percentage error in density

Units and Measurements in past papers

53 questions from this chapter have appeared across 25 exam years.