Answer
$$\frac{v_A}{v_B}=\frac{\sqrt2}{2}$$
Work Step by Step
In uniform circular motion, we have $$v^2=a_c\times r$$
Here, we see that $r_B=2r_A$ and $a_B=a_A$
Therefore, $$\frac{v^2_A}{v^2_B}=\frac{a_A\times r_A}{a_B\times r_B}=\frac{1}{2}$$ $$\frac{v_A}{v_B}=\frac{\sqrt2}{2}$$
