Q. Two particles of masses $m_{a}\ and\ m_{b}$ and same charge are projected in a perpendicular magnetic field. They travel along circular paths of radius $r_{a}\ and\ r_{b}$ such that $r_{a} > r_{b}.$ Then which is true?
A) $m_{a}\ v_{a} > m_{b}\ v_{b}$
B) $m_{a} > m_{b}\ and\ \ v_{a} > \ v_{b}$
C) $m_{a} = m_{b}\ and\ \ v_{a} = \ v_{b}$
D) $m_{b}\ v_{b} > m_{a}\ v_{a}$
Explanation
(a) Radius of circular path $r_{a} = \frac{m_{a}\ v_{a}}{qB}$
And $r_{b} = \frac{m_{b}\ v_{b}}{qB}$
According to question
$r_{a} > r_{b}$
$\therefore\ \ \frac{m_{a}\ v_{a}}{qB} > \ \frac{m_{b}\ v_{b}}{qB}$
or $m_{a}v_{a} > m_{b}v_{b}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.