Q 12-04-089JEE MainJEE Main 2024 (29 Jan, Shift 2)Easy
Two particles $X$ and $Y$ having equal charges are being accelerated through the same potential difference. Thereafter, they enter normally in a region of uniform magnetic field and describe circular paths of radii $R_1$ and $R_2$ respectively. The mass ratio of $X$ and $Y$ is:
Answer: (B) $\left(\dfrac{R_1}{R_2}\right)^2$
After acceleration, $p = \sqrt{2mqV}$, so
$$R = \frac{p}{qB} = \frac{\sqrt{2mqV}}{qB} \;\Rightarrow\; R \propto \sqrt m$$
$$\frac{m_X}{m_Y} = \left(\frac{R_1}{R_2}\right)^2$$
Solution by Sreeraj P, M.Sc Physics