Two particles of masses ma and mb and same charge are projected in a perpendicular magnetic field. They travel along circular paths of radius ra and rb such that ra rb . Then which is true?

Question

Two particles of masses ma and mb and same charge are projected in a perpendicular magnetic field. They travel along circular paths of radius ra and rb such that ra > rb . Then which is true? (A)  mava > mbvb  (B)  ma > mb and va > vb  (C)  ma = mb and va > vb  (D)  mbvb > mava

Tardigrade Admin · Accepted Answer

Radius of circular path ra= (mava/qB) and rb= (mbvb/qB) According to questions ra>rb ∴ (mava/qB)> (mbvb/qB) or mava>mbvb

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?

$m_{a} v_{a} > m_{b} v_{b}$

$m_{a} > m_{b}$ and $v_{a} > v_{b}$

$m_{a} = m_{b}$ and $v_{a} > v_{b}$

$m_{b} v_{b} > m_{a} v_{a}$

Radius of circular path $r_{a} = \frac{m _{a} v _{a}}{qB}$
and $r_{b} = \frac{m _{b} v _{b}}{qB}$
According to questions
$r_{a} > r_{b}$
$∴ \frac{m _{a} v _{a}}{qB} > \frac{m _{b} v _{b}}{qB}$
or $m_{a} v_{a} > m_{b} v_{b}$

Q. Two particles of masses ma​ and mb​ and same charge are projected in a perpendicular magnetic field. They travel along circular paths of radius ra​ and rb​ such that ra​>rb​ . Then which is true?

ma​va​>mb​vb​

ma​>mb​ and va​>vb​

ma​=mb​ and va​>vb​

mb​vb​>ma​va​