A wire of resistance 5 Ω is stretched to three times its original length. The new resistance of the wire is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 45 Ω
When a wire is stretched, its volume stays the same, so its cross-sectional area falls in the same ratio as its length rises. The resistivity does not change, because the material is the same. Putting \( A = V/l \) into \( R = \rho l/A \):
\( \displaystyle R = \frac{\rho l}{A} = \frac{\rho l^{2}}{V} \quad\Rightarrow\quad R \propto l^{2} \)
\( l' = 3l \)
\( R' = 3^{2} \times 5\,\Omega = 45\,\Omega \)
Note: A similar question was also asked in CUET (UG) 2023 on 13-06-2023 (Slot 2) and on 05-06-2023 (Slot 3).