Question

A deuteron and a proton moving with equal kinetic energy enter into to a uniform magnetic field at right angle to the field. If $r_{d}$ and $r_{p}$ are the radii of their circular paths respectively, then the ratio $\frac{r_{d}}{r_{p}}$ will be $\sqrt{ x }: 1$ where $x$ is _____

Answer 1

$R =\frac{ mv }{ q _{ B }}$
$R _{ D }=\frac{\left(2 m _{ P }\right) v _{ D }}{ eB }$
$R _{ P }=\frac{\left( m _{ P }\right) v _{ P }}{ e B }$
$\frac{ R _{ D }}{ R _{ P }}=\frac{2 v _{ D }}{ v _{ P }}=\frac{2 v _{ D }}{\sqrt{2} v _{ D }}=\frac{\sqrt{2}}{1}$
$\frac{1}{2}(2 mp ) v _{ D }^{2}=\frac{1}{2} m _{ P } \cdot v _{ P }^{2}$
$\sqrt{2} v _{ D }= v _{ P }$
$x =2$