A proton, a deuteron and an $\alpha-$particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is
A$1: \sqrt{2}: \sqrt{2}$
B$1: 1: \sqrt{2}$
C$\sqrt{2}: 1: 1$
D$1: \sqrt{2}: 1$
JEE MAIN 2022, Medium
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D$1: \sqrt{2}: 1$
d $R =\frac{\sqrt{2 \,km }}{ qB } \propto \frac{\sqrt{ m }}{ q }$
$\frac{\sqrt{ m }}{ e }: \frac{\sqrt{2 \,m }}{ e }: \frac{\sqrt{4\, m }}{2 e }$
$1: \sqrt{2}: 1$
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