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Two particles 1 and 2 of masses $m_{1}$ and $m_{2}$ having the same charge q, are moving with velocities $v_{1}$ and $v_{2}$ respectively in a plane. They describe circular paths of radii $r_{1}$ and $r_{2}$ in a uniform magnetic field B which is directed perpendicular to this plane as shown in figure. Then

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$\frac{m_{1}}{m_{2}} = \frac{v_{1}}{v_{2}}$

$m_{1} v_{1} > m_{2} v_{2}$

$m_{1} v_{1} < m_{2} v_{2}$

$m_{1} v_{1} = m_{2} v_{2}$

answer is C.

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Detailed Solution

$\frac{{mv}^{2}}{r} = qvB \Rightarrow mv = qrB ∴ m_{1} v_{1} = {qr}_{1} B and m_{2} v_{2} = {qr}_{2} B \frac{m_{1} v_{1}}{m_{2} v_{2}} = \frac{r_{1}}{r_{2}} < 1 (∵ r_{1} < r_{2})$

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