Question

Two particles $A$ and $B$ having equal charges $+6$ C after being accelerated through the same potential difference enter in a region of uniform magnetic field and describe circular paths of radii $2cm$ and $3cm$ respectively. The ratio of mass of $A$ to that of $B$ is :

• A. $\frac{1}{3}$
• B. $\frac{1}{2}$
• C. $\frac{4}{9}$
• D. $\frac{9}{5}$

Answer 1

The correct option is C $\frac{4}{9}$

Since, $r=\frac{\sqrt{2mqV}}{qB}=\sqrt{\frac{2mV}{q{B}^2}}=\frac{r_1}{r_2}=\sqrt{\frac{m_1}{m_2}}$

$\frac{m_1}{m_2}=r_1^2{r}_2^2$

Hence, $\frac{m_1}{m_2}=\frac{(2{)}^2}{\left(3^2\right)}=\frac{4}{9}$