Question

Two particles $X$ and $Y$ having equal charges after being accelerated through same potential difference enter a region of uniform magnetic field and describe a circular paths 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)

Radius of circular path traced by a particle $r=\frac{m v}{B q}$
Kinetic energy $K =\frac{1}{2} mv ^{2}= eV$
$\therefore r=\frac{\sqrt{m^{2} v^{2}}}{B q}=\frac{\sqrt{2 m K}}{B q} $
Or $ r=\frac{\sqrt{2 m e V}}{B q} $
$\Rightarrow m \propto r^{2}$
Thus we get the ratio of masses of $X$ to $Y \frac{m_{1}}{m_{2}}=\left[\frac{r_{1}}{r_{2}}\right]^{2}$