Two charged particles having charges 1 $μC$ and -1 $μC$ and of mass 50 gm each are held at rest while their separation is 2 m. Find the speed of the particles when their separation is 1 m.

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$\frac{1}{5} m / s$

$\frac{3}{5} m / s$

$\frac{3}{10} m / s$

$\frac{2}{7} m / s$

answer is C.

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Detailed Solution

From conservation of energy

The potential energy will be converted into kinetic energy of the bodies

$\begin{aligned} \frac{q_{1} q_{2}}{4 {πε}_{0}} [\frac{1}{r_{1}} - \frac{1}{r_{2}}] = 2 [\frac{1}{2} {mv}^{2}] \\ \Rightarrow v = \sqrt{\frac{q_{1} q_{2}}{4 {πε}_{0} m} [\frac{1}{r_{1}} - \frac{1}{r_{2}}]} \end{aligned}$

On putting the values we get

v= $\frac{3}{10} m / s$

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