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 describe circular paths of radii $R_1$ and $R_2$, respectively. The ratio of the mass of $X$ to that of $Y$ is

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

Answer 1

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

$\frac{1}{2}m{v}^2=qVorv=\sqrt{\frac{2qV}{m}}$
Centripetal force, $\frac{m{v}^2}{R}=qvB\Rightarrow v=\left(\frac{qB}{m}\right)R$
$\sqrt{\frac{2qV}{m}}=\left(\frac{qB}{m}\right)R\Rightarrow R={\left(\frac{2mV}{q}\right)}^{1/2}\times \frac{1}{B}$
Here $V,q,B$ are constant. Hence $m\propto R^2$
o, $\frac{m_1}{m_2}={\left(\frac{R_1}{R_2}\right)}^2$