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 masses 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

Answer: (C)

$(R_1/R_2{)}^2$

We know,

$R=\frac{\sqrt{2mqV}}{qB}$

As q,B,V are same

$R\propto \sqrt{m}$

$\frac{R_1}{R_2}=\sqrt{\frac{m_1}{m_2}}$

$\frac{m_1}{m_2}=\frac{(R_1{)}^2}{(R_2{)}^2}$

Option $\text{C}$ is the correct answer.