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.
• C.
• D. 1836

Answer 1

The correct option is B

F = qE. S = $\frac{1}{2}a{t}^2$ $\Rightarrow$ S = $\frac{1}{2}\left(\frac{qE}{m}\right)t^2$

$S_e=\frac{1}{2}\left(\frac{qE}{m_e}\right)(t_1{)}^2$ and $S_p=\frac{1}{2}\left(\frac{qE}{m_p}\right)(t_2{)}^2$

As, $S_e=S_p$ $\Rightarrow$ $\frac{{t_1}^2}{m_e}=\frac{{t_2}^2}{m_p}$ $\Rightarrow$ $\frac{t_2}{t_1}={\left(\frac{m_p}{m_e}\right)}^{\frac{1}{2}}$