Question

Two particles X and Y having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describes circular path of radius $R_1$ and $R_2$ respectively. The ratio of mass of X to that of Y is

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

Answer 1

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

$r=\frac{\sqrt{2mk}}{qB}=\frac{1}{B}\sqrt{\frac{2mV}{q}}\Rightarrow r\propto \sqrt{m}\Rightarrow \frac{m_1}{m_2}={\left(\frac{R_1}{R_2}\right)}^2$