JEE MAIN - Physics (2021 - 25th July Evening Shift - No. 5)
Two ions having same mass have charges in the ratio 1 : 2. They are projected normally in a uniform magnetic field with their speeds in the ratio 2 : 3. The ratio of the radii of their circular trajectories is :
1 : 4
4 : 3
3 : 1
2 : 3
Explanation
$$R = {{mv} \over {qB}} \Rightarrow {{{R_1}} \over {{R_2}}} = {{{{m{v_1}} \over {{q_1}B}}} \over {{{m{v_2}} \over {{q_2}B}}}} = {{{v_1}} \over {{q_1}}} \times {{{q_2}} \over {{v_2}}} = {{{q_2}} \over {{q_1}}} \times {{{v_1}} \over {{v_2}}}$$
$$ = {2 \over 1} \times \left( {{2 \over 3}} \right) = {4 \over 3}$$
$$ = {2 \over 1} \times \left( {{2 \over 3}} \right) = {4 \over 3}$$
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