Q. 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 $t_{1}/t_{2\ }$is nearly equal to
A) 1
B) $\sqrt{M_{p}/M_{e}}$
C) $\sqrt{M_{e}/M_{p}}$
D) 1836
Explanation
(b) From $s = ut + \frac{1}{2}at^{2} = \frac{1}{2}at^{2}$
$t = \sqrt{\begin{array}{r}
\frac{2s}{a} \\
\
\end{array}}\ $
As $s$ is same,
$\therefore\ t \propto \ \begin{array}{r}
\frac{1}{\sqrt{a}}\ \\
\
\end{array}$
$\frac{t^{2}}{t^{1}} = \sqrt{\frac{a^{1}}{a^{2}}} = \sqrt{\ \frac{F_{e}/M_{e}}{F_{p}/M_{p}}} = \sqrt{\frac{M_{p}}{M_{e}}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.