A proton and an aparticle ( with their masses in the ratio of $1: 4$ and charges in the ratio of $1:

Question

A proton and an aparticle ( with their masses in the ratio of $1: 4$ and charges in the ratio of $1: 2$ ) are accelerated from rest through a potential difference $V$. If a uniform magnetic field ( $B$ ) is set up perpendicular to their velocities, the ratio of their radii $r_p: r_a$ of the circular paths described by them will be

Professor PC Thomas Classes · Answer

$r = \frac{\sqrt{2mK}}{qB} = \frac{\sqrt{2mqV}}{qB} \propto \sqrt{\frac{m}{q}}$. Ratio is $\sqrt{\frac{1/4}{1/2}} = \frac{1}{\sqrt{2}}$.