A proton and an α particle enter a uniform magnetic field with same velo

Question

A proton and an $α$ particle enter a uniform magnetic field with same velocity, then ratio of the radii of path describe by them will be?

Options:

A . 1 : 2

B . 1 : 1

C . 2 : 1

D . None of these

Answer: Option A
:
A
By using

r = \frac{m v}{q B}

;

v \to

same,

B \to

same

\Rightarrow r \propto \frac{m}{q} \Rightarrow \frac{r_{p}}{r_{α}} = \frac{m_{p}}{m_{α}} \times \frac{q_{α}}{q_{p}} = \frac{m_{p}}{4 m_{p}} \times \frac{2 q_{p}}{q_{p}} = \frac{1}{2}

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