Question

An electron is accelerated from rest through a potential different $V$. Its final speed is proportional to

• A. $V$
• B. $V^2$
• C. $\sqrt{V}$
• D. $\frac{1}{\sqrt{V}}$

Answer 1

The correct option is C

$\sqrt{V}$

work done = $qV$

According to the work-energy theorem, work done is equal to a change in Kinetic Energy

$$\begin{gathered} W=K_f-K_i \\ Finalkineticenergy-intitalkineticenergy \end{gathered}$$

$W=\frac{1}{2}m{v}^2-\frac{1}{2}m{u}^2$

Here $u=0$, which is at rest

$$\begin{gathered} W=\frac{1}{2}m{v}^2 \\ W=qV=\frac{1}{2}m{v}^2 \\ {v}^2\alpha V \\ v\alpha \sqrt{V} \end{gathered}$$

Therefore the correct option in (C), $\sqrt{V}$

option $C$ is the right answer.