Two equal and opposite charges of masses m1 and m2 are accelerated in a uniform electric field through the same distance. What is the ratio of their accelerations, if their ratio of masses is m1m2 = 0.5 ?

We know that, force experienced by charge in electric field

$F_{1} = q_{1} E = m_{1} a_{1}$ …(i)

$F_{2} = q_{2} E = m_{2} a_{2}$ …(ii)

As, $q_{1} = q_{2} \Rightarrow F_{1} = F_{2}$

From Eqs. (i) and (ii), we get

$\frac{a_{1}}{a_{2}} = \frac{F_{1} / m_{1}}{F_{2} / m_{2}} = \frac{F \cdot m_{2}}{F \cdot m_{1}}$

$\Rightarrow \frac{a_{1}}{a_{2}} = \frac{m_{2}}{m_{1}} = \frac{1}{0.5} = \frac{10}{5} = 2 (∵ \frac{m_{1}}{m_{2}} = 0.5)$

Two equal and opposite charges of masses m₁ and m₂are accelerated in a uniform electric field through the same distance. What is the ratio of their accelerations, if their ratio of masses is $\frac{m_{1}}{m_{2}} = 0.5 ?$