Question

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. $\sqrt{3}:1$
• C. 2 : 1
• D. $1:\sqrt{2}$

Answer 1

Answer: (D)

Acceleration of $\alpha$ - particle,
$a_r=\frac{qE}{m}=\frac{2eE}{4}$
Acceleration of photon, $a_p=\frac{eE}{1}$
They travel same distances in time $t_1$ and $t_2$.
$\Rightarrow \frac{1}{2}\left(\frac{2eE}{1}\right)t_1^2=\frac{1}{2}\left(\frac{eE}{1}\right)t_2^2$
$\Rightarrow \frac{t_2^2}{t_1^2}=\frac{1}{2}$
$\Rightarrow \frac{t_2}{t_1}=\frac{1}{\sqrt{2}}$