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. $2{\pi }^{2}m{v}^2{r}^2$
• C. $2{\pi }^2{m}^2{v}^2{r}^2$
• D. ${\pi }^{2}m{v}^2{r}^2$
• E. ${\pi }^2{m}^2{v}^2{r}^2$

Answer 1

The correct option is B $2{\pi }^{2}m{v}^2{r}^2$

Given,
r = the outside radius of the dees
v = the speed of the particle when travelingon a path of this radius
m = the mass of pi own
The kinetic energy of particles accelerated. In a cyclotron
$K=2{\pi }^2{m}^2{v}^2{r}^2$