A particle of mass \(1 \times 10^{-27} \mathrm{~kg}\) and charge \(1 \times 10^{-16} \mathrm{C}\) enters the uniform magnetic field within the solenoid, at speed \(1000 \mathrm{~ms}^{-1}\). The velocity vector makcs an angle \(60^{\circ}\) with the axis of solenoid. The solenoid has 5000 turns along its length and carries current \(5 \mathrm{~A}\). The number of revolution the particle makes along the helical path within the solenoid by the time it emerges from solenoid's opposite end 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.