A wire of length 10 m and diameter 0.4 mm has a resistance of \( 2\,\Omega \). The resistivity of the wire is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 2.5\times10^{-8}\,\Omega\,\mathrm{m} \)
The resistance of a wire is \( R = \rho l/A \), so the resistivity is \( \rho = RA/l \), with \( A \) the circular cross-section of diameter \( d \).
\( \displaystyle d = 0.4\,\mathrm{mm} = 4\times10^{-4}\,\mathrm{m}, \qquad A = \frac{\pi d^{2}}{4} = \frac{3.14 \times 16\times10^{-8}}{4} = 1.256\times10^{-7}\,\mathrm{m^{2}} \)
\( \displaystyle \rho = \frac{R A}{l} = \frac{2 \times 1.256\times10^{-7}}{10} = 2.5\times10^{-8}\,\Omega\,\mathrm{m} \)
Note: A similar question was also asked in CUET (UG) 2026 on 21-05-2026 (Slot 2).