Question

Two charged particles having charge $1\, \mu C$ and $-1\, \mu C$ and of mass $50\, g$ each are held at rest while their separation is $2\, m$. Find the relative velocity of the particles when their separation is $0.5\, m$.

• A. $\frac{1}{5} m / s$
• B. $\frac{\sqrt{3}}{5} m / s$
• C. $\frac{3 \sqrt{3}}{5} m / s$
• D. $\frac{3 \sqrt{3}}{10} m / s$

Answer 1

Answer: (C)

Speed of both will be same at any time,
$(K E+P E)_{f}=(K E+P E)_{i}$
$2\left(\frac{1}{2} m v^{2}\right)-\frac{9 \times 10^{9} \times 10^{-12}}{0.5}$
$=-\frac{9 \times 10^{9} \times 10^{-12}}{2}+0$
$m v^{2}=9 \times 10^{-3}\left[\frac{1}{0.5}-\frac{1}{2}\right]$
Putting $m=50 / 1000 ; v=\frac{3 \sqrt{3}}{10} m / s$