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Byju's Answer

Standard XII

Physics

Circular Kinematics

Two particles...

Question

Two particles A and B of masses $m_{A}$ and $m_{B}$ respectively and having the same charge are moving in a plane. A uniform magnetic field exists perpendicular to this plane. The speed of the particles are $v_{A}$ and $v_{B}$ respectively, and the trajectories are as shown in the figure. Then

m_{A} v_{A} < m_{B} v_{B}

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m_{A} v_{A} > m_{B} v_{B}

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m_{A} < m_{B}

and

v_{A} < v_{B}

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m_{A} = m_{B}

and

v_{A} = v_{B}

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Solution

The correct option is B $m_{A} v_{A} > m_{B} v_{B}$
When a charged particle is moving at right angle to the magnetic field, then a force acts on it which behaves as a centripetal force and moves the particle in circular path.
But, $r = \frac{p}{q B}$
Radius of B is less than radius of A.
$r_{B} < r_{A}$
$∴ p_{B} < p_{A}$
$\Rightarrow m_{B} v_{B} < m_{A} v_{A}$
$\Rightarrow m_{A} v_{A} > m_{B} v_{B}$ .

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