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Time Period Independent of Amplitude

Two ions havi...

Question

Two ions having masses in the ratio 1:1 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

A

4:3

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B

2:3

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C

3:1

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D

1:4

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Solution

The correct option is A 4:3
Answer is A.
In magnetic field
$r = \frac{m V}{q B}$

so, $\frac{r_{1}}{r_{2}} = \frac{m_{1} V_{1}}{q_{1} B_{1}}$ x $\frac{q_{2} B_{2}}{m_{2} V_{2}}$

$= (\frac{m_{1}}{m_{2}}) (\frac{V_{1}}{V_{2}}) (\frac{q_{2}}{q_{1}}) (\frac{B_{2}}{B_{1}})$

$= (\frac{1}{1}) (\frac{2}{3}) (\frac{2}{1}) (\frac{1}{1})$ (as given in problem)

$= \frac{4}{3}$

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