Maximum kinetic energy of the positive ion in the cyclotron is
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(c)${K_{\max }} = \frac{1}{2}m{v^2}$ and ${r_0} = \frac{{mv}}{{qB}}$ $==>$ $v = \frac{{qB{r_0}}}{m}$
$==>$ ${K_{\max }} = \frac{1}{2}m{\left( {\frac{{qB{r_0}}}{m}} \right)^2} = \frac{{{q^2}{B^2}r_0^2}}{{2m}}$
$==>$ ${K_{\max }} = \frac{1}{2}m{\left( {\frac{{qB{r_0}}}{m}} \right)^2} = \frac{{{q^2}{B^2}r_0^2}}{{2m}}$
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