Chapter 19 - Magnetism - Learning Path Questions and Exercises - Exercises - Page 688: 10

(c) $m_{A}=\frac{1}{2}m_{B}$

The force caused by magnetic field is to be equated to the centripetal force. Thus, $F=\frac{mv^{2}}{r}$ Since two particles A and B have identical charge and speed, $Fa=Fb$ or, $\frac{m_{A}v^{2}}{r_{A}}=\frac{m_{B}v^{2}}{r_{B}}$ or, $\frac{m_{A}}{r_{A}}=\frac{m_{B}}{r_{B}}$ or, $\frac{m_{A}}{m_{B}}=\frac{r_{A}}{r_{B}}=\frac{25}{50}=\frac{1}{2}$ Hence, (c) is the answer.