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Two ions having masses in the ratio $1 : 2$ and charges $1 : 2$ are projected into uniform magnetic field perpendicular to the field with speeds in the ratio $2 : 3$ . The ratio of the radii of circular paths along which the two particles move is

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$4 : 3$

$2 : 3$

$3 : 1$

$1 : 2$

answer is B.

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Detailed Solution

$m_{1} : m_{2} = 1 : 2, q_{1} : q_{2} = 1 : 2, v_{1} : v_{2} = 2 : 3$ $R = \frac{mv}{qB} \Rightarrow \frac{R_{1}}{R_{2}} = \frac{m_{1}}{m_{2}} \frac{v_{1}}{v_{2}} \frac{q_{1}}{q_{2}}$

$= \frac{1}{2} \times \frac{2}{3} \times \frac{2}{1} = 2 : 3$

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