Q 12-04-016NEETJEE MainMedium
A proton and an alpha particle have the same kinetic energy and move perpendicular to the same uniform magnetic field. The ratio of the radii of their circular paths, $r_p : r_\alpha$, is
Answer: (B) $1 : 1$
$r = \dfrac{mv}{qB} = \dfrac{\sqrt{2mK}}{qB}$.
Proton: $\dfrac{\sqrt{2mK}}{eB}$. Alpha (mass $4m$, charge $2e$): $\dfrac{\sqrt{8mK}}{2eB} = \dfrac{\sqrt{2mK}}{eB}$.
The radii are equal, so the ratio is $1 : 1$.
Solution by Sreeraj P, M.Sc Physics