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Two particles X and Y having equal charges after being accelerated through the same potential difference, enter a region of uniform magnetic field and describe circular paths of radii $R_{1} and R_{2}$ respectively. The ratio of the masses X and Y is

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{(\frac{R_{1}}{R_{2}})}^{\frac{1}{2}}

(\frac{R_{2}}{R_{1}})

{(\frac{R_{1}}{R_{2}})}^{2}

(\frac{R_{1}}{R_{2}})

answer is C.

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Detailed Solution

The K.E of the particles remains constant

$K .E = \frac{1}{2} {mv}^{2} = constant, r = \frac{mv}{Bq} \Rightarrow v = \frac{Bqr}{m}$

$\frac{1}{2} {mv}^{2} = \frac{q^{2} B^{2} r^{2}}{2 m} = constant$

$q^{2} B^{2} r^{2} \propto 2 m$

$\frac{m_{1}}{m_{2}} \propto {(\frac{R_{1}}{R_{2}})}^{2}$

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