Question

Two particles $X$ and $Y$ having equal charges, are accelerated through the same potential difference. They enter a region of a uniform magnetic field and describe a circular path of radii $r_{1}$ and $r_{2}$ respectively. The ratio of the mass of $X$ to that of $Y$ is

• A. $\frac{r_{1}}{r_{2}}$
• B. $\sqrt{\frac{r_{1}}{r_{2}}}$
• C. $\left[\frac{r_{2}}{r_{1}}\right]^{2}$
• D. $\left[\frac{r_{1}}{r_{2}}\right]^{2}$

Answer 1

Answer: (D)

The force acting on the particle inside the magnetic field is $F_{B}=qvBsin \theta $
$\theta =90^\circ $ , $F_{B}=qvB$
This provides the necessary centripetal force $F_{c}=\frac{m v^{2}}{r}$
$\therefore \, \, \frac{m v^{2}}{r}=qvB\Rightarrow r=\frac{m v}{q B}$ $= \sqrt{\frac{2 m q V}{q B}}$
$\frac{r_{1}}{r_{2}} = \sqrt{\frac{m_{x}}{m_{y}}}$
$\frac{m_{x}}{m_{y}}=\left(\frac{r_{1}}{r_{2}}\right)^{2}$