Question

Two α - particles have the ratio of their velocities as 3:2 on entering the field. If they move in different circular paths, then the ratio of the radii of their paths is:

• A. $2:3$
• B. 3:2
• C. 9:4
• D. 4:9

Answer 1

The correct option is B

3:2

Step 1:Given parameters

$\frac{v_1}{v_2}=\frac{3}{2}$

Step 2:To Find:

The ratio of the radii of their paths

Step 3:Calculate ratio of the radii of their paths:

The lorentz force acting on the particle acts as a centripetal force.

$qvB=\frac{m{v}^2}{r}$

Hence, $r\propto V$.

Here, $r$ is the radius,$v$ is velocity, $q$ is charge value, $B$ is magnetic field, and $m$is mass.

$$\begin{gathered} \frac{r_1}{r_2}=\frac{v_1}{v_2} \\ =\frac{3}{2} \end{gathered}$$

Hence, option(B) is correct.