A ∝ particle and a proton enters a region of uniform magnetic field B with same momentum at right angle to magnetic field. The ratio of the radii of the circular paths of ∝ particle to proton is

1 : 2

The correct answer is Option (2) → 1 : 2

The radius (r) of the path is -

$r=\frac{mv}{qB}=\frac{P}{qB}$ [$P=mv$ = Momentum]

$∴\frac{r_α}{r_P}=\frac{\frac{P_α}{q_αB}}{\frac{P_P}{q_PB}}=\frac{P_α}{P_P}×\frac{q_P}{q_α}$

$=\frac{q_P}{q_α}=\frac{1}{2}$ [$P_α=P_P$ given]