Question

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 `(r_p/r_alpha)` is ______.

विकल्प

• `3/4`

• `4/3`

• `8/9`

• `9/8`

Answer 1

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 `(r_p/r_alpha)` is `bbunderline(9/8)`.

Explanation:

`r = (mV)/(qB)`

For proton, `r_p = (mV_p)/(qB)`

For alpha article, `r_alpha = (4mV_alpha)/(2qB)`

= `(2mV_alpha)/(qB)`

∴ `r_p/r_alpha = V_p/(2V_alpha)`

= `1/2 xx (9/4)`

= `9/8`