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# Two particles $X$ and $Y$ equal charges enter a region of uniform magnetic field after being accelerated through the same potential difference and describe circular paths of radii $R_X$ and $R_Y$ respectively. The ratio of their masses is

$\begin {array} {1 1} (a)\;\large\frac{R_X}{R_Y} & \quad (b)\;\bigg( \large\frac{R_X}{R_Y}\bigg)^2 \\ (c)\;\large\frac{R_Y}{R_X} & \quad (d)\;\bigg( \large\frac{R_X}{R_Y}\bigg)^{\large\frac{1}{2}} \end {array}$

$R = \large\frac {mv}{qB} $$= \large\frac{m}{qB} \sqrt \frac{2Vq}{m} = \large\frac{1}{B} \sqrt \frac{2Vm}{q}$$ \;\propto \sqrt m$
$\therefore \large\frac{R_X}{R_Y} $$= \large\sqrt \frac{m_X}{m_Y}$$\rightarrow \large\frac{m_X}{m_Y}$$= \large(\frac{R_X}{R_Y})^2$
edited Mar 14, 2014