Setting the centripetal force equal to the Lorentz force gives
$\begin{align*}m_e \frac{v^2}{r} = e v B\end{align*}$
This can then be solved for $v$ :
$\begin{align*}v = \frac{e B r}{m_e}\end{align*}$
So, if $r_1/r_2 = 1/3$ , then
$\begin{align*}\frac{v_1}{v_2} = \frac{e B r_1/m_e}{e B r_2/m_e} = \frac{r_1}{r_2} = \boxed{\frac{1}{3}}\end{align*}$
Therefore, answer (B) is correct.

Solution to 2008 Problem 71