To identical particles of charge Q each are connected by a massless spring of force constant k that placed over a smooth horizontal surface they are released when unstreched if maximum extension of the spring is are the value of k is neglect gravitational effect

$
\begin{aligned}
&\text { After an elongation of r, the separation between the charges will be ' } 2 r^{\prime}\\
&\begin{gathered}
\frac{1}{4 \pi \epsilon_0} \times \frac{q^2}{2 r}=\frac{1}{2} k r^2 \\
k=\sqrt{\frac{q^2}{4 \pi \epsilon_0 r^3}}=\frac{q}{2 r} \sqrt{\frac{1}{\pi \epsilon_0 r}}
\end{gathered}
\end{aligned}
$

$ \begin{aligned} &\text { After an elongation of r, the separation between the charges will be ' } 2 r^{\prime}\\ &\begin{gathered} \frac{1}{4 \pi \epsilon_0} \times \frac{q^2}{2 r}=\frac{1}{2} k r^2 \\ k=\sqrt{\frac{q^2}{4 \pi \epsilon_0 r^3}}=\frac{q}{2 r} \sqrt{\frac{1}{\pi \epsilon_0 r}} \end{gathered} \end{aligned} $

$ \begin{aligned} &\text{After an elongation of } r,\text{ the separation between the charges will be } 2r.\\ &\begin{gathered} \frac{1}{4\pi\epsilon_0}\times\frac{q^2}{2r}=\frac{1}{2}kr^2 \\ k=\frac{q^2}{4\pi\epsilon_0r^3} \end{gathered} \end{aligned} $

$ \begin{aligned} &\text{After an elongation of } r,\text{ the separation between the charges will be } 2r.\\ &\begin{gathered} \frac{1}{4\pi\epsilon_0}\times\frac{q^2}{2r}=\frac{1}{2}kr^2 \\ k=\frac{q^2}{4\pi\epsilon_0r^3} \end{gathered} \end{aligned} $

$ \begin{aligned} &\text{After an elongation of } r,\text{ the separation between the charges will be } 2r.\\ &\begin{gathered} \frac{1}{4\pi\epsilon_0}\times\frac{q^2}{2r}=\frac{1}{2}kr^2 \\ k=\frac{q^2}{4\pi\epsilon_0r^3} \end{gathered} \end{aligned} $

$ \begin{aligned} &\text{After an elongation of } r,\text{ the separation between the charges will be } 2r.\\ &\begin{gathered} \frac{1}{4\pi\epsilon_0}\times\frac{q^2}{2r}=\frac{1}{2}kr^2 \\ k=\frac{q^2}{4\pi\epsilon_0r^3} \end{gathered} \end{aligned} $

$ \begin{aligned} &\text { After an elongation of r, the separation between the charges will be ' } 2 r^{\prime}\\ &\begin{gathered} \frac{1}{4 \pi \epsilon_0} \times \frac{q^2}{2 r}=\frac{1}{2} k r^2 \\ k=\sqrt{\frac{q^2}{4 \pi \epsilon_0 r^3}}=\frac{q}{2 r} \sqrt{\frac{1}{\pi \epsilon_0 r}} \end{gathered} \end{aligned} $

$

\begin{aligned}

&\text { After an elongation of r, the separation between the charges will be ' } 2 r^{\prime}\\

&\begin{gathered}

\frac{1}{4 \pi \epsilon_0} \times \frac{q^2}{2 r}=\frac{1}{2} k r^2 \\

k=\sqrt{\frac{q^2}{4 \pi \epsilon_0 r^3}}=\frac{q}{2 r} \sqrt{\frac{1}{\pi \epsilon_0 r}}

\end{gathered}

\end{aligned}

$