Question

An electron of mass $m_e$ initially at rest moves through a certain distance in a uniform electric field in time $t_1$. A proton of mass $m_p$, also initially at rest, takes time $t_2$ to move through an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio $\frac{t_2}{t_1}$ is nearly equal to

• A. 1
• B. $\sqrt{\frac{m_p}{m_e}}$
• C. $\frac{m_p}{m_e}$
• D. 1836

Answer 1

The correct option is B $\sqrt{\frac{m_p}{m_e}}$

$s=\frac{1}{2}a{t}^2$
$\Rightarrow s=\frac{1}{2}\left(\frac{aE}{m}\right)t^2$
$\Rightarrow t\propto \sqrt{m}$
$\Rightarrow \frac{t_2}{t_1}=\sqrt{\frac{m_p}{m_e}}$