A rectangular coil of \(300\) turns has an average area of \(25 \mathrm{~cm} \times 10 \mathrm{~cm}\). The coil rotates with a speed of \(50 \mathrm{~cps}\) in uniform magnetic field of strength \(4 \times 10^{-2} \mathrm{~T}\) about an axis perpendicular to the field. The peak value of the induced emf \((\) in \(\mathrm{V})\) is

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.