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A charged particle of charge $+ Q$ and mass $M$ is projected perpendicular to a uniform magnetic field as shown. It undergoes a deviation of $60 °$ while moving through the magnetic field.

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If its mass would have been $M / 2$ , it would undergo a deviation of $180 °$

If its mass would have been $3 M$ , it would undergo a deviation of $180 °$

If it had negative charge, it would deflect downwards with same angle of deviation

If its mass would have been $2 M$ , it would undergo a deviation of $30 °$

answer is A, D.

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Detailed Solution

$\sin 60 ° = \frac{d}{m v} \times q B$

If mass is doubled, radius is doubled

$\sin θ = \frac{\sin 60 °}{3} = \frac{\sqrt{3}}{4}$

If mass is $3 M$ , radius is $3$ times

$\sin θ' = \frac{\sin 60 °}{3} = \frac{1}{2 \sqrt{3}}$

If mass is halved,

$R = \frac{m v}{2 q B} \Rightarrow \frac{m v}{q B} = \frac{2 d}{\sqrt{3}} \Rightarrow R = \frac{2 d}{\sqrt{3}} \times \frac{1}{2} = \frac{d}{\sqrt{3}}$

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