Given $$\mathrm{m}_1=\mathrm{m}_2$$

$$\text { and } \frac{r_1}{r_2}=\frac{3}{4}$$

As centripetal force $$\mathrm{F}=\frac{\mathrm{mv}^2}{\mathrm{r}}$$

In order to have constant (same in this question) centripetal force

$$\begin{aligned} & \mathrm{F}_1=\mathrm{F}_2 \\ & \frac{\mathrm{m}_1 \mathrm{v}_1^2}{\mathrm{r}_1}=\frac{\mathrm{m}_2 \mathrm{v}_2^2}{\mathrm{r}_2} \\ & \Rightarrow \frac{\mathrm{v}_1}{\mathrm{v}_2}=\sqrt{\frac{\mathrm{r}_1}{\mathrm{r}_2}}=\frac{\sqrt{3}}{2} \end{aligned}$$