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

The correct option is D ${\left[\frac{r_1}{r_2}\right]}^2$

Radius of circular path traced by a particle $r=\frac{mv}{Bq}$

Kinetic energy $K=\frac{1}{2}m{v}^2=eV$

$\therefore$ $r=\frac{\sqrt{m^2{v}^2}}{Bq}=\frac{\sqrt{2mK}}{Bq}$

Or $r=\frac{\sqrt{2meV}}{Bq}$

$⟹$ $m\propto r^2$

Thus we get the ratio of masses of $X$ to $Y$ $\frac{m_1}{m_2}=[\frac{r_1}{r_2}{]}^2$