An $\alpha$-particle (mass $4 amu$ ) and a singly charged sulfur ion (mass $32 amu$ ) are initially at rest. They are accelerated through a potential $V$ and then allowed to pass into a region of uniform magnetic field which is normal to the velocities of the particles. Within this region, the $\alpha$-particle and the sulfur ion move in circular orbits of radii $r_\alpha$ and $r_5$, respectively. The ratio $\left(r_s / r_\alpha\right)$ is. . . . .$(4)$
IIT 2021, Easy
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$r =\frac{ mV }{ qB }=\frac{\sqrt{2 mqV }}{ qB }$
$\frac{ P ^2}{2 m }= K E= qV$
$\frac{ r _{ s }}{ r _\alpha}=\sqrt{\frac{32}{1} \times \frac{2}{4}}=4$
$\frac{ r _{ s }}{ r _\alpha}=4$
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