The power required for an engine to maintain a constant speed of \(50 \mathrm{~m} \mathrm{~s}^{-1}\) for a train of mass \(3 \times 10^6 \mathrm{~kg}\) on rough rails is
(The coefficient of kinetic friction between the rails and wheels of the train is 0.05 and acceleration due to gravity \(=10 \mathrm{~m} \mathrm{~s}^{-2}\) )

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.