Question

A particle of mass $2 \, g$ and charge $1 \, \mu C$ is held at rest on a frictionless horizontal surface at a distance of $1 \, m$ from a fixed charge $1 \, mC$ . 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. $100 \, ms^{- 1}$
• B. $90 \, ms^{- 1}$
• C. $60 \, ms^{- 1}$
• D. $45 \, ms^{- 1}$

Answer 1

Answer: (B)

From the conservation of mechanical energy,
$U_{i}+K_{i}=U_{f}+K_{f}$
$\frac{K q_{1} q_{2}}{r_{1}}+0=\frac{K q_{1} q_{2}}{r_{2}}+\frac{1}{2}mv^{2}$
$\left(9 \times 1 0^{9}\right) \, \times \left(1 \times 1 0^{- 3}\right)\left(1 \times 1 0^{- 6}\right)\left[\frac{1}{1} - \frac{1}{10}\right]=\frac{1}{2}\left(2 \times 1 0^{- 3}\right)v^{2}$
$\sqrt{\frac{9 \times 9}{10} \times \frac{2}{2 \times 1 0^{- 3}}}=v$
$v=90 \, ms^{- 1}$