In a cyclotron angular speed of a charge particle is independent of…
(A) Mass of the particle
(B) Linear speed of the particle
(C) Magnetic field
(D) Charge of the particle

Hint: In this question we have to determine the factor of a cyclotron particle accelerator which does not have any effect on the angular speed of the cyclotron. A cyclotron is a particle accelerator used to accelerate the positively charged particles such as Protons. It consists of two circular hollow electrodes in the shape of the “D” alphabet. The particle is accelerated due to the electric field between the two electrodes. The acceleration of the particle happens between the two circular electrodes when the particle comes in contact with the magnetic field.

Complete step by step answer:
Given:
For a cyclotron particle accelerator having a positively charged particle of mass $m$ and charge $q$ moving in the circular path inside the magnetic field $B$, the relationship formula for the angular speed $\omega $ of the particle is given by –
$\omega = \dfrac{{qB}}{m}$
So, from this formula it is clear that, the angular speed $\omega $ of the particle in the cyclotron depends upon the mass of the particle $m$ , the magnetic field $B$ and the charge of the particle $q$ only, it does not depend upon the linear speed of the particle.

Therefore, the angular speed of a charge particle in a cyclotron is independent of the linear speed of the particle.

Thus, the correct option is (B).

Note:
The particle inside the cyclotron moves along a spiral path in the direction outwards from the centre of the path. Which means that the particle never really forms a circular path so we cannot determine the radius of this movement of the particle. Therefore, we cannot relate the linear velocity with the angular velocity of the particle.