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  4. Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is 6: 5 and their respective masses ratio is 9: 4. Then, the ratio of their charges will be :

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Q. Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is $6: 5$ and their respective masses ratio is $9: 4$. Then, the ratio of their charges will be :

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Solution:

Radius of circular path $R =\frac{\sqrt{2 mk }}{ qB }$
$ q =\frac{\sqrt{2 mk }}{ RB } $
$ \frac{ q _1}{ q _2}=\sqrt{\frac{ m _1}{ m _2}} \times \frac{ R _2}{ R _1}=\sqrt{\frac{9}{4}} \times \frac{5}{6}=\frac{5}{4}$