Electrostatics 1 Question 9
9. 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 $t _2 / t _1$ is nearly equal to
(1997, 1M)
(a) 1
(b) $\left(m _p / m _e\right)^{1 / 2}$
(c) $\left(m _e / m _p\right)^{1 / 2}$
(d) 1836
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Answer:
Correct Answer: 9. (c)
Solution:
- Electrostatic force, $F _e=e E$ (for both the particles)
But acceleration of electron, $a _e=F _e / m _e$ and
acceleration of proton, $a _p=F _e / m _p$
$$ S=\frac{1}{2} a _e t _1^{2}=\frac{1}{2} a _p t _2^{2} \Rightarrow \therefore \quad \frac{t _2}{t _1}=\sqrt{\frac{a _e}{a _p}}=\sqrt{\frac{m _p}{m _e}} $$
