Q144 / 160 · AP EAMCET 2018 (23 Apr Shift 2) · Physics
A proton and an $\alpha$-particle start from rest in a uniform electric field. The ratio of times taken by them to travel the same distance in the field is
- A$\sqrt{5}: \sqrt{2}$
- B$\sqrt{3}: 1$
- C2 : 1
- Correct answerD$1: \sqrt{2}$
Solution
Acceleration of $\alpha$-particle, $a_r=\frac{q E}{m}=\frac{2 e E}{4}$ Acceleration of photon,
$$
a_p=\frac{e E}{1}
$$
They travel same distances in time $t_1$ and $t_2$.
$$
\Rightarrow \frac{1}{2}\left(\frac{2 e E}{4}\right) t_1^2=\frac{1}{2}\left(\frac{e E}{1}\right) t_2^2 \Rightarrow \frac{t_2^2}{t_1^2}=\frac{1}{2} \Rightarrow \frac{t_2}{t_1}=\frac{1}{\sqrt{2}}
$$
Hence, the correct answer is option: 'D'.