Q 12-04-166JEE MainJEE Main 2021 (25 Feb, Shift 1)Medium
A proton, a deuteron and an $\alpha$ particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them ______ is and their speed is ______ in the ratio.
Answer: (A) 2 : 1 : 1 and 4 : 2 : 1
Masses $m : 2m : 4m$, charges $e : e : 2e$. With equal momentum $p$, $v = p/m$:
$$v_p : v_d : v_\alpha = 1 : \tfrac12 : \tfrac14 = 4 : 2 : 1$$
Force $F = qvB$ (velocity perpendicular to $B$): $e(4) : e(2) : 2e(1) = 4 : 2 : 2 = 2 : 1 : 1$.
Solution by Sreeraj P, M.Sc Physics