A steel wire and a copper wire are joined end to end having equal cross-sections. The elongation of two wires is found to be equal under tension. What is the ratio of the length of the steel to the length of copper wire? (Young modulus of steel $=2.0\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$ and, Young modulus of copper $=1.1\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.