Question

A particle of mass 2g and charge $1\mu C$ is held at a distance of 1m from a fixed charge $1\mu C$. If the particle is released it will be repelled. The speed of particle when it is at a distance of 10 metre from the fixed charge is

• A. 90 m/s
• B. 100 m/s
• C. 45 m/s
• D. 55 m/s

Answer 1

Answer: (A)

Potential at $1m$ from the charge
$V_A=\frac{K\times 10^{-3}}{1}$
Potential at $10m$ from the charge
$V_B=\frac{K\times 10^{-3}}{10}=K\times 10^{-4}$
potential diff $=V_A-V_B$
$=K\left(10^{-3}-10^{-4}\right)$
Its velocity at $10m$ is $V$, then
$\frac{1}{2}\times m{v}^2=\left(V_A-V_B\right)q$
$\frac{1}{2}\times 2\times 10^{-3}{v}^2$
$=K\times 10^{-6}\left(1-\frac{1}{10}\right)\times 10^{-3}$
$v^2=K\times \frac{9}{10}\times 10^{-6}$
$9\times 10^9\times \frac{9}{10}\times 10^{-6}$
$=81\times 100$
$v=90m/\sec$