In the cyclotron, as the radius of the circular path of the charged particle increases, ($\omega$ = angular velocity, $V$ = linear velocity)

If the maximum value of accelerating potential provided by a radio frequency oscillator is $12 \, kV$,the number of revolutions made by a proton in a cyclotron to achieve one-sixth of the speed of light is ....... .
$[m_p = 1.67 \times 10^{-27} \, kg, e = 1.6 \times 10^{-19} \, C, c = 3 \times 10^8 \, m/s]$

$A$ cyclotron's oscillator frequency is $n$ and the radius of the dees is $r$. The operating magnetic field $(B)$ for accelerating protons of charge $q$ and the kinetic energy of the protons produced by the accelerator are respectively ($m$ and $v$ are the mass and velocity of the proton).

$A$ charged particle is subjected to acceleration in a cyclotron as shown. The charged particle undergoes an increase in its speed:

$A$ cyclotron is used to accelerate

In a cyclotron,the time taken by an ion to describe a semicircular path in a dee is