A proton and an $\alpha$-particle enter with the same velocity $\vec{v}$ in a uniform magnetic field $\vec{B}$ such that $\vec{v} \perp \vec{B}$. The ratio of the radii of their paths is : (A) $2$ (B) $\frac{1}{2}$ (C) $\frac{1}{4}$ (D) $4$