Question

Two particles A and B having equal charges +6C, after being accelerated through the same potential difference, enter 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. $\frac{4}{9}$
• B. $\frac{9}{5}$
• C. $\frac{1}{2}$
• D. $\frac{1}{3}$

Answer 1

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

$r=\frac{\sqrt{2mE}}{eB}=\sqrt{\frac{2mV}{e{B}^2}}$
Two particles each of charge 6C under same magnetic field
$r\propto \sqrt{m}$
$\frac{r_1}{r_2}=\sqrt{\frac{m_1}{m_2}}$
squaring both sides
$\frac{m_1}{m_2}={\left(\frac{r_1}{r_2}\right)}^2=\frac{4}{9}$