A proton and an $\alpha$ -particle, having kinetic energies $K _{ p }$ and $K _{\alpha},$ respectively, enter into $a$ magnetic field at right angles.
The ratio of the radii of trajectory of proton to that of $\alpha$ -particle is $2: 1 .$ The ratio of $K _{ p }: K _{\alpha}$ is :
JEE MAIN 2021, Medium
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$r =\frac{ mv }{ qB }=\frac{ p }{ qB } \quad \frac{ m _{\alpha}}{ m _{ p }}=4$
$\frac{ r _{ p }}{ r _{\alpha}}=\frac{ p _{ p }}{ q _{ p }} \frac{ q _{\alpha}}{ p _{\alpha}}=\frac{2}{1}$
$\frac{ p _{ p }}{ p _{\alpha}}=\frac{2 q _{ p }}{ q _{\alpha}}=2\left(\frac{1}{2}\right)$
$\frac{ p _{ p }}{ p _{\alpha}}=1$
$\frac{ K _{ p }}{ K _{\alpha}}=\frac{ p _{ p }^{2}}{ p _{\alpha}^{ p }} \frac{ m _{\alpha}}{ m _{ p }}=(1)$ (4)
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