Two ions having same mass have charges in the ratio 1: 2 . They are...

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,

Options

A $1: 4$
B $4: 3$
C $3: 1$
D $2: 3$

Correct answer

B. $4: 3$

Step-by-step solution

$R = \dfrac{mv}{qB} ⇒ \dfrac{{R}_{1}}{{R}_{2}} = \dfrac{\dfrac{m{v}_{1}}{{q}_{1}B}}{\dfrac{m{v}_{2}}{{q}_{2}B}} = \dfrac{{v}_{1}}{{q}_{1}} \times \dfrac{{q}_{2}}{{v}_{2}} = \dfrac{{q}_{2}}{{q}_{1}} \times \dfrac{{v}_{1}}{{v}_{2}}$

$= \dfrac{2}{1} \times \left(\dfrac{2}{3}\right) = \dfrac{4}{3}$

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