A unit scale is to be prepared whose length does not change with temperature and remains \(20\,cm\), using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constant. If length of brass is \(40\,cm\) and length of iron will be\(...cm\) \(\left(\alpha_{\text {iron }}=1.2 \times 10^{-5} K ^{-1}\right.\) and \(\left.\alpha_{\text {brass }}=1.8 \times 10^{-5} K ^{-1}\right)\).

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.