What should be the ratio of velocities of proton to that of an alpha particle so that they trace a path of same radius in a perpendicular magnetic field ?

2 : 1

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

The radius of a charged particle's circular motion in a magnetic field is-

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

$⇒\frac{v_p}{v_α}=\frac{m_αq_p}{m_pq_α}$  [B → Constant]

$∴\frac{v_p}{v_α}=\frac{4m_αq_p}{m_p2q_α}=\frac{2}{1}$   $[∵m_α=4m_p,q_α=2e=2q_p]$