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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 mass of X to that of Y is

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

{\frac{R_{1}}{R_{2}}}_{}

(

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

{\frac{R_{1}}{R_{2}}}_{}

answer is C.

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Detailed Solution

The ratio of mass of X to that of Y is (

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

Radius of circular path traced by a particle
r=

\frac{mv}{Bq}

Where ,

m = mass

v = velocity of charged particle

q = charge

r = radius

B = strength of magnetic field

Kinetic energy

K = \frac{1}{2} m v^{2} = eV

r = \frac{\sqrt{m^{2} v^{2}}}{Bq}

r = \frac{\sqrt{2 mK}}{Bq}

r = \frac{\sqrt{2 meV}}{Bq}

m

directly proportional to

r^{2}

We get

\frac{m_{1}}{m_{2}} = (\frac{r_{1}}{r_{2}})^{2}

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