A charged particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charged particle increases to $4$ times its initial value. What will be the ratio of new radius to the original radius of circular path of the charged particle
JEE MAIN 2022, Medium
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radius of paerticle in cyclotron
$r =\frac{\sqrt{2 mK . E .}}{ qB }$
So ratio of new radius to original
$\frac{ r _{ n }}{ r _{0}}=\sqrt{\frac{( K \cdot E .)_{ n }}{( K \cdot E )_{0}}}=\sqrt{4} \Rightarrow 2: 1$
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