# Two ions having

Question:

Two ions having same mass have charges in the ratio $1: 2$. They are projected normally in a uniform magnetic field with their speeds in the ratio $2: 3$. The ratio of the radii of their circular trajectories is:

1. $1: 4$

2. $4: 3$

3. $3: 1$

4. $2: 3$

Correct Option: , 2

Solution:

$\mathrm{R}=\frac{\mathrm{mv}}{\mathrm{qB}} \Rightarrow \frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}=\frac{\frac{\mathrm{mv}_{1}}{\mathrm{q}_{1} \mathrm{~B}}}{\frac{\mathrm{mv}_{2}}{\mathrm{q}_{2} \mathrm{~B}}}=\frac{\mathrm{v}_{1}}{\mathrm{q}_{1}} \times \frac{\mathrm{q}_{2}}{\mathrm{v}_{2}}=\frac{\mathrm{q}_{2}}{\mathrm{q}_{\mathrm{l}}} \times \frac{\mathrm{v}_{1}}{\mathrm{v}_{2}}$

$=\frac{2}{1} \times\left(\frac{2}{3}\right)=\frac{4}{3}$