$A$ cyclotron is used to accelerate

In a cyclotron,a charged particle:

The maximum kinetic energy of a positive ion in a cyclotron is given by:

Describe the motion of a charged particle in a cyclotron if the frequency of the radio frequency $(rf)$ field were doubled.

Discuss the motion of a charged particle in a uniform magnetic field with initial velocity perpendicular to the magnetic field. $OR$ Explain the principle of a cyclotron.

$A$ charged particle moves along a circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charged particle increases to $4$ times its initial value. What will be the ratio of the new radius to the original radius of the circular path of the charged particle?