### Magnetic Effects Of Current Question 8

#### Question 8 - 2024 (29 Jan Shift 2)

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 describes circular paths of radii $R _1$ and $R _2$ respectively. The mass ratio of $X$ and $Y$ is :

(1) $\left(\frac{R _2}{R _1}\right)^{2}$

(2) $\left(\frac{R _1}{R _2}\right)^{2}$

(3) $\left(\frac{R _1}{R _2}\right)$

(4) $\left(\frac{R _2}{R _1}\right)$

## Show Answer

#### Answer: (2)

#### Solution:

$R=\frac{mv}{qB}=\frac{p}{qB}=\frac{\sqrt{2 m(KE)}}{qB}=\frac{\sqrt{2 mqV}}{qB}$

$R \propto \sqrt{m}$

$m \propto R^{2}$

$\frac{m _1}{m _2}=\left(\frac{R _1}{R _2}\right)^{2}$