Question

Two equal and opposite charges of masses $m_1$ and $m_2$ are accelerated in an uniform electric field through the same distance. What is the ratio of their accelerations if their ratio of masses is $\frac {m_1}{m_2}=0.5$?

• A. $\frac{a_{1}}{a_{2}}=0.5$
• B. $\frac{a_{1}}{a_{2}}=1$
• C. $\frac{a_{1}}{a_{2}}=2$
• D. $\frac{a_{1}}{a_{2}}=3$

Answer 1

Answer: (C)

Given, $\frac{m_{1}}{m_{2}}=0.5$
$ \Rightarrow F_{1}=F_{2}=F$
(force experiened by equal charge in electric field)
We know that
$F_{1}=q_{1} E\,\,\,\,\,\dots(i)$
$F_{2}=q_{2} E$ (as $q_{1}=q_{2} )\,\,\,\,\,\dots(ii)$
From Eqs. (i) and (ii), we get
$\frac{a_{1}}{a_{2}}=\frac{F_{1} / m_{1}}{F_{2} / m_{2}}$
$\Rightarrow \frac{a_{1}}{a_{2}}=\frac{F \cdot m_{2}}{F \cdot m_{1}}$
$\frac{a_{1}}{a_{2}}=\frac{m_{2}}{m_{1}}=\frac{1}{0.5}=\frac{10}{5}=2$
$\therefore \frac{a_{1}}{a_{2}}=2$