Mathematics In Physics Question 1
Question 1 - 2024 (01 Feb Shift 1)
The radius ( $r$ ), length $(l)$ and resistance $(R)$ of a metal wire was measured in the laboratory as
$r=(0.35 \pm 0.05) cm$
$R=(100 \pm 10) ohm$
$l=(15 \pm 0.2) cm$
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:
$\rho=R \frac{\rho}{\ell}$
$$ \begin{aligned} & \frac{\Delta \rho}{\rho}=\frac{\Delta R}{R}+2 \frac{\Delta r}{r}+\frac{\Delta \ell}{\ell} \\ & =\frac{10}{100}+2 \times \frac{0.05}{0.35}+\frac{0.2}{15} \\ & =\frac{1}{10}+\frac{2}{7}+\frac{1}{75} \\ & \frac{\Delta \rho}{\rho}=39.9 \% \end{aligned} $$
