Two particles X and Y having equal charges, after being accelerated...

When a charge particle is allowed to move in a uniform magnetic field, then it describes spiral or circular path \begin{array}{l} \text{ Centripetal force, } \frac{\mathrm{mv}^{2}}{\mathrm{R}}=\mathrm{qvB} \quad \therefore \\ \mathrm{v}=\left(\frac{\mathrm{qB}}{\mathrm{m}} \mathrm{R}\right) \\ \text{ Hence, } \sqrt{\frac{2 \mathrm{q} \mathrm{V}}{\mathrm{m}}}=\left(\frac{\mathrm{qB}}{\mathrm{m}}\right) \mathrm{R}\left[\because \mathrm{V}=\sqrt{\frac{2 \mathrm{qV}}{\mathrm{m}}}\right] \\ \Rightarrow \mathrm{R}=\left(\frac{2 \mathrm{mV}}{\mathrm{q}}\right)^{1 / 2} \times \frac{1}{\mathrm{~B}} \\ \text{ or, } \mathrm{m} \propto \mathrm{R}^{2} \end{array} $[\because \mathrm{V}, \mathrm{q}$ and $\mathrm{B}$ are constant $]$ $$\text{ or, } \frac{\mathrm{m}_{1}}{\mathrm{~m}_{2}}=\left(\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}\right)^{2}$$