Two particles X and Y having equal charges are being accelerated … - Vidyadip

MCQ

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 :

A
$\left(\frac{R_2}{R_1}\right)^2$
B
$\left(\frac{ R _1}{ R _2}\right)^2$
C
$\left(\frac{ R _1}{ R _2}\right)$
D
$\left(\frac{ R _2}{ R _1}\right)$

✓

Answer

$R =\frac{ mv }{ qB }$
$=\frac{ p }{ qB }$
$=\frac{\sqrt{2 m( KE )}}{ qB }$
$=\frac{\sqrt{2 mqV }}{ qB }$
$R \propto \sqrt{ m }$
$m \propto R ^2$
$\frac{m_1}{m_2}=\left(\frac{ R _1}{ R _2}\right)^2$

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