Cyclotron And Frequency Of Revolution

As discussed in NCERT Class 12, Chapter 4 (Moving Charges and Magnetism), a cyclotron accelerates charged particles using a fixed-frequency alternating voltage. The period of circular motion is $T=\frac{2\pi m}{qB}$ and the cyclotron frequency is $f=\frac{qB}{2\pi m}$. Notice that neither the speed nor the radius appears in this expression: as the particle speeds up, its radius grows proportionally, keeping the time per revolution constant. This is exactly why a single fixed-frequency supply can keep accelerating the particle, which is the operating principle of the cyclotron. The option 'charge value' is wrong because $q$ clearly appears in $f$. The option 'mass value' is wrong because $m$ appears in the denominator. The option 'magnetic field strength' is wrong because $B$ appears directly. Plausibility check: since a faster particle traces a larger circle in the same time, the constancy of $f$ with respect to speed and radius is self-consistent, confirming the first option. Dimensionally, $\frac{qB}{2\pi m}$ gives $\frac{\text{C}\cdot \text{T}}{\text{kg}}=\frac{\text{C}\cdot \text{kg/(Ccdotps)}}{\text{kg}}={\text{s}}^{-1}$, correctly a frequency, and this speed-independence is precisely why the cyclotron eventually fails only at relativistic speeds, where the mass effectively grows and the resonance condition finally breaks down.