A charge particle moves along circular path in a uniform magnetic...

Radius of a charged particle moving in a magnetic field perpendicular to its velocity is given by, $R = \dfrac{mv}{qB}$.

$mv$ can be written in terms of kinetic energy as $mv = \sqrt{2m\left(KE\right)}$. Therefore,

$R = \dfrac{mv}{qB} = \dfrac{\sqrt{2m\left(KE\right)}}{qB}$

$⇒ R ∝ \sqrt{KE} ⇒ \dfrac{{R}_{2}}{{R}_{1}} = \sqrt{\dfrac{{K}_{2}}{{K}_{1}}} = \sqrt{\dfrac{4}{1}} = \dfrac{2}{1}$