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 maxim

Question

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

Accepted Answer

Density $\rho = \frac{m}{V} = \frac{m}{\pi r^2 l}$. The relative error is $\frac{\Delta \rho}{\rho} = \frac{\Delta m}{m} + 2\frac{\Delta r}{r} + \frac{\Delta l}{l}$. Substituting values: $\frac{0.002}{0.4} + 2(\frac{0.001}{0.3}) + \frac{0.02}{5} = 0.005 + 0.0066 + 0.004 = 0.0156$. Percentage error $\approx 1.6\%$.

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