Question

Two particles $X$ and $Y$ having equal charges, after being accelerated through the same potential differences, enter in a region of uniform magnetic field and describe circular paths of radii $R_1$ and $R_2$ respectively. The ratio of the mass of $X$ to that of $Y$ is :

• A. $(\frac{R_1}{R_2}{)}^{1/2}$
• B. $(\frac{R_1}{R_2}{)}^{-1}$
• C. $(\frac{R_1}{R_2}{)}^2$
• D. $(\frac{R_1}{R_2})$

Answer 1

The correct option is C $(\frac{R_1}{R_2}{)}^2$

Since the particle is accelerated through $V$ volts
$\because \frac{m{v}^2}{2}=qV$
$mv=\sqrt{2mqV}$
$R=\frac{mv}{qB}$
So, $R_1=\frac{\sqrt{2m_{1}qV}}{qB}$
$R_2=\frac{\sqrt{2m_{2}qV}}{qB}$
$\frac{m_1}{m_2}=(\frac{R_1}{R_2}{)}^2$