Q 12-04-141JEE MainJEE Main 2022 (24 Jun, Shift 2)Medium
A proton, a deuteron and an $\alpha$-particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is:
Answer: (B) $1 : \sqrt2 : 1$
$r = \dfrac{mv}{qB} = \dfrac{\sqrt{2mK}}{qB}\propto\dfrac{\sqrt m}{q}$ for equal $K$.
$$r_p : r_d : r_\alpha = \frac{\sqrt1}{1} : \frac{\sqrt2}{1} : \frac{\sqrt4}{2} = 1 : \sqrt2 : 1$$
Solution by Sreeraj P, M.Sc Physics