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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
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Verified Answer
The correct answer is:
$1: \sqrt{2}$
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 $t_2$.
$$
\Rightarrow \frac{1}{2}\left(\frac{2 e E}{4}\right) t_1^2=\frac{1}{2}\left(\frac{e E}{1}\right) t_2^2 \Rightarrow \frac{t_2^2}{t_1^2}=\frac{1}{2} \Rightarrow \frac{t_2}{t_1}=\frac{1}{\sqrt{2}}
$$
$$
a_p=\frac{e E}{1}
$$
They travel same distances in time $t_1$ and $t_2$.
$$
\Rightarrow \frac{1}{2}\left(\frac{2 e E}{4}\right) t_1^2=\frac{1}{2}\left(\frac{e E}{1}\right) t_2^2 \Rightarrow \frac{t_2^2}{t_1^2}=\frac{1}{2} \Rightarrow \frac{t_2}{t_1}=\frac{1}{\sqrt{2}}
$$
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