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Circular Kinematics

Two particles...

Question

Two particles of masses $m_{a}$ and $m_{b}$ and same charge are projected in a perpendicular magnetic field. Travel travel along circular paths of radius $r_{a}$ and $r_{b}$ such that $r_{a} > r_{b}$ . That which is true ?

A

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

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B

m_{a} > m_{b}

and

v_{a} > v_{b}

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C

m_{a} = m_{b}

and

v_{a} > v_{b}

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D

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

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Solution

The correct option is B $m_{a} v_{a} > m_{b} v_{b}$
The centripetal force is provided to the charged particle by the magnetic field.
Thus, $\frac{m v^{2}}{r} = q v B$

$⟹$ radius of the circular path= $r = \frac{m v}{q B}$

For $r_{a} > r_{b}$ for same charge and magnetic field,

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

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