A metallic wire of resistance R and resistivity \( \rho \) is cut into six equal parts. Now each part is stretched to six times its length. The new resistance and resistivity of each part will be, respectively:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 6R \) and \( \rho \)
Resistivity is a property of the material (at a given temperature), so cutting or stretching does not change it: it stays \( \rho \). The resistance \( R = \rho l/A \) changes with the shape. When a wire is stretched its volume stays the same, so the area falls as the length rises.
Cutting into six equal parts: each part has length \( l/6 \) and the same area, so
\( \displaystyle R_1 = \frac{R}{6} \)
Stretching each part to six times its length: length \( \times 6 \), area \( \div 6 \), so the resistance becomes \( 6 \times 6 = 36 \) times.
\( \displaystyle R_2 = 36 \times \frac{R}{6} = 6R \)