Question

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

• A. $100m{s}^{-1}$
• B. $90m{s}^{-1}$
• C. $60m{s}^{-1}$
• D. $45m{s}^{-1}$

Answer 1

Answer: (B)

From the conservation of mechanical energy,
$U_i+K_i=U_f+K_f$
$\frac{K{q}_1{q}_2}{r_1}+0=\frac{K{q}_1{q}_2}{r_2}+\frac{1}{2}m{v}^2$
$\left(9\times 10^9\right)\times \left(1\times 10^{-3}\right)\left(1\times 10^{-6}\right)\left[\frac{1}{1}-\frac{1}{10}\right]=\frac{1}{2}\left(2\times 10^{-3}\right)v^2$
$\sqrt{\frac{9\times 9}{10}\times \frac{2}{2\times 10^{-3}}}=v$
$v=90m{s}^{-1}$