A blacksmith fixes circular iron frame on the wooden wheel of a bullock cart. The diameter of wooden wheel and circular iron frame are \(5.012 \mathrm{~m}\) and \(5 \mathrm{~m}\) respectively at \(27^{\circ} \mathrm{C}\). The temperature (in \({ }^{\circ} \mathrm{C}\) ) to which the iron ring must be heated so as to fit the wooden wheel is (Coefficient of linear expansion of iron \(=1.2 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}\) )

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.