PhysicsA proton and an alpha particle move in circular orbits in a uniform magnetic field. Their speeds are in the ratio of 9:4. The ratio of radii of their circular orbits rprα is

A proton and an alpha particle move in circular orbits in a uniform magnetic field. Their speeds are in the ratio of 9:4. The ratio of radii of their circular orbits $\frac{r_{p}}{r_{α}}$ is

A
3/4
B
4/3
C
8/9
D
9/8

Solution:

Given, $\frac{v_{p}}{v_{α}} = \frac{9}{4}$
$\frac{r_{p}}{r_{α}} = \frac{\frac{m_{p} \cdot v_{p}}{B \cdot q_{p}}}{\frac{m_{α} \cdot v_{α}}{B \cdot q_{α}}} = \frac{m_{p} \cdot q_{α} \cdot v_{p}}{m_{α} \cdot q_{p} \cdot v_{α}} = \frac{{mm}_{p} \cdot 2 q_{p} \cdot v_{p}}{4 {mm}_{p} \cdot q_{p} \cdot v_{α}} = \frac{9}{8}$
$[As we know m_{α} = 4 m_{p} and q_{α} = 2 q_{p}]$

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A proton and an alpha particle move in circular orbits in a uniform magnetic field. Their speeds are in the ratio of 9:4. The ratio of radii of their circular orbits $\frac{r_{p}}{r_{α}}$ is

Solution:

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