Assume the charge initially on spheres A and B is $Q$ . After sphere C is touched to sphere A, the charges on sphere A is $Q/2$ , the charge on sphere B is $Q$ , and the charge on sphere C is $Q/2$ . After sphere C is touched to sphere B, the charge on sphere A is $Q/2$ , the charge on sphere B is $3Q/4$ and the charge on sphere C is $3Q/4$ . The force between spheres A and B is given by Coulomb's law
$\begin{align*}\left|\mathbf{F}\right| = \frac{Q_A Q_B}{4 \pi \epsilon_0 \left|\mathbf{r_A} - \mathbf{r_B} \right|^2}\end{alig...$
So, the initial force is
$\begin{align*}F = \frac{Q^2}{4 \pi \epsilon_0 \left|\mathbf{r_A} - \mathbf{r_B} \right|^2}\end{align*}$
and the final force is
$\begin{align*} \frac{3Q^2/8}{4 \pi \epsilon_0 \left|\mathbf{r_A} - \mathbf{r_B} \right|^2} = \boxed{3 F/8}\end{align*}$
Therefore, answer (D) is correct.

Solution to 1996 Problem 24