Mathematics In Physics Question 1
Question 1 - 2024 (01 Feb Shift 1)
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 :
(1) $25.6 %$
(2) $39.9 %$
(3) $37.3 %$
(4) $35.6 %$
Show Answer
Answer: (2)
Solution:
$\rho=\mathrm{R} \frac{\rho}{\ell}$
$$ \begin{aligned} & \frac{\Delta \rho}{\rho}=\frac{\Delta \mathrm{R}}{\mathrm{R}}+2 \frac{\Delta \mathrm{r}}{\mathrm{r}}+\frac{\Delta \ell}{\ell} \ & =\frac{10}{100}+2 \times \frac{0.05}{0.35}+\frac{0.2}{15} \ & =\frac{1}{10}+\frac{2}{7}+\frac{1}{75} \ & \frac{\Delta \rho}{\rho}=39.9 % \end{aligned} $$
