A wire of length 10 m and diameter 0.4 mm has a resistance of 2 Ω. The resistivity of the wire is

$2.5 × 10^{-8} Ωm$

The correct answer is Option (1) → $2.5 × 10^{-8} Ωm$

$\text{Given: Length } L = 10~\text{m},~ \text{diameter } d = 0.4~\text{mm} = 0.0004~\text{m},~ R = 2~\Omega$

$\text{Radius: } r = \frac{d}{2} = 0.0002~\text{m}$

$\text{Cross-sectional Area: } A = \pi r^2 = \pi (0.0002)^2 = 1.2566 \times 10^{-7}~\text{m}^2$

$\text{Resistance: } R = \frac{\rho L}{A} \Rightarrow \rho = \frac{R A}{L}$

$\rho = \frac{2 \cdot 1.2566 \times 10^{-7}}{10}$

$\rho = 2.5132 \times 10^{-8}~\Omega \cdot \text{m}$

$\text{Answer: } \rho = 2.51 \times 10^{-8}~\Omega \cdot \text{m}$