Question

If the radius of the dees of cyclotron is $r$, then the kinetic energy of a proton of mass $m$ accelerated by the cyclotron at an oscillating frequency $v$ is

• A. $4 \pi^2 \,m^2 \,v^2\, r^2$
• B. $4 \pi^2\, m v^2 \,r^2$
• C. $ 2 \pi^2 \,m v^2 \,r^2$
• D. $ \pi^2 \,m v^2 \,r^2$
• E. $ \pi^2 \,m^2 \,v^2 \,r^2$

Answer 1

Answer: (C)

Given,
$r=$ the outside radius of the dees
$V=$ the speed of the particle when travelling in a path of this radius
$m=$ the mass of proton
Kinetic energy of particles accelerated in a cyclotron
$K=2 \pi^{2}\, m v^{2}\, r^{2}$