Q. Two particles $X\ and\ Y$ having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describes circular path of radius $R_{1}\ and\ R_{2}$ respectively. The ratio of mass of $X\ to\ that\ of\ Y\ is$
A) $\left( R_{1}/R_{2} \right)^{1/2}$
B) $R_{2}/R_{1}$
C) $\left( R_{1}/R_{2} \right)^{2}$
D) $R_{1}/R_{2}$
Explanation
(c) As, $qV = \frac{1}{2}mv^{2}\ \ or\ v = \sqrt{\frac{2qV}{m}};$ when particle describes a circular path of radius $R$ in the magnetic field
$q\ v\ B = \frac{mv^{2}}{R}\ \ \ \ \ \ \ \ \ or\ \ \ \ R = \frac{m\ v^{2}}{q\ v\ B} = \frac{m\ v}{q\ B}$
Or $R = \frac{m}{q\ B}\ \sqrt{\frac{2\ q\ V}{m}} = \frac{1}{B}\sqrt{\frac{2\ V\ m}{q}}$
$ie,\ \ R \propto \ \sqrt{m}\ \ \ \ \ \ \ \ \ \ \therefore\frac{m_{x}}{m_{y}} = \left( \frac{R_{1}}{R_{2}} \right)^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.