A proton and an alpha particle of the same velocity enter in turn a region of uniform magnetic field, acting perpendicular to their direction of motion. The ratio of the radii of the circular paths described by the particles, respectively, would be

1 : 2

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

$r = \frac{mv}{qB}$

$\frac{r_p}{r_\alpha} = \frac{m_p/q_p}{m_\alpha/q_\alpha}$

$m_p = m,\quad q_p = e$

$m_\alpha = 4m,\quad q_\alpha = 2e$

$\frac{r_p}{r_\alpha} = \frac{m/e}{4m/2e}$

$\frac{r_p}{r_\alpha} = \frac{m}{e} \cdot \frac{2e}{4m}$

$\frac{r_p}{r_\alpha} = \frac{1}{2}$

The ratio is $1:2$.