JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement
The radius ( \(\mathrm{r})\), length \((l)\) and resistance \((\mathrm{R})\) of a metal wire was measured in the laboratory as \(\mathrm{r}=(0.35 \pm 0.05) \mathrm{cm}\) \(\mathrm{R}=(100 \pm 10) \mathrm{ohm}\) \(l=(15 \pm 0.2) \mathrm{cm}\) The percentage error in resistivity of the material of the wire is _______.
- A \(25.6 \%\)
- B \(39.9 \%\)
- C \(37.3 \%\)
- D \(35.6 \%\)
Answer & Solution
Correct Answer
(B) \(39.9 \%\)
Step-by-step Solution
Detailed explanation
\(\rho={R} \frac{\rho}{\ell}\) \(\frac{\Delta \rho}{\rho}=\frac{\Delta \mathrm{R}}{\mathrm{R}}+2 \frac{\Delta \mathrm{r}}{\mathrm{r}}+\frac{\Delta \ell}{\ell}\) \(=\frac{10}{100}+2 \times \frac{0.05}{0.35}+\frac{0.2}{15}\) \(=\frac{1}{10}+\frac{2}{7}+\frac{1}{75}\)…
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