JEE MAIN - Physics (2022 - 25th July Morning Shift - No. 11)
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 :
8 : 5
5 : 4
5 : 3
8 : 7
Explanation
We know that $$R = {{mv} \over {Bq}} = \sqrt {{{2mK} \over {Bq}}} $$
$$\Rightarrow$$ Ratio of radii $$ = {{{R_1}} \over {{R_2}}} = \sqrt {{{{m_1}} \over {{m_2}}}} {{{q_2}} \over {{q_1}}}$$
$$ \Rightarrow {6 \over 5} = \sqrt {{9 \over 4}} {{{q_2}} \over {{q_1}}}$$
$$ \Rightarrow {{{q_1}} \over {{q_2}}} = {3 \over 2} \times {5 \over 6} = {5 \over 4}$$
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