Concept:Resistance is proportionally linked to length and cross-sectional area. Usually stretching implies volume remains constant (decreasing area), but the prompt places a strict hypothetical constraint.
Formula:$$ R = \rho \frac{L}{A} $$
Solution:- The prompt explicitly states "but its radius stays constant". This means Area (\( A = \pi r^2 \)) does not change.
- If Area is constant, Resistance is directly and linearly proportional to Length (\( R \propto L \)).
- Since Length is doubled (\( L' = 2L \)), the resistance simply doubles.
- New resistance = 2R.
Why other options are incorrect:- Opt C: 4R would be correct ONLY IF the wire's volume was conserved (meaning the area naturally shrank by half as it stretched). The prompt's constraint explicitly overrides this.
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