Question

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 $r_s$, respectively. The ratio of $\frac{r_s}{r_{\alpha }}$ is

Answer 1

For a charged particle projected into uniform magnetic field, radius of path is given by
$r=\frac{\sqrt{2mqV}}{qB}\Rightarrow r\propto \sqrt{\frac{m}{q}}$
$\Rightarrow \frac{r_s}{r_{\alpha }}=\sqrt{\frac{m_s}{m_{\alpha }}\left(\frac{q_{\alpha }}{q_s}\right)}=\sqrt{\frac{32\left(2\right)}{4\left(1\right)}}=4$