A and B are two identical spherical charged bodies which repel each other with force F, kept at a finite distance apart A third uncharged sphere of the same size is brought in contact with sphere B and removed. It is then kept at mid-point of A and B find the magnitude of force on C.

The correct option is C F

$A$ and $B$ are two identical spherical charged bodies which repel each other with force $=F$

finite distance =

From the figure again, you can see $C$ is placed at $\frac{r}{2}$. Now see the direction of force due to $A$ on $C$.

$F_{AC}$ and force due to $B$ on $C$ $F_{BC}$ from simple coulomb's law you can answer as follows

$F_{AC}=\frac{KQ.Q/2}{\frac{r^2}{y}}=\frac{2{KQ}^2}{r^2}=2F$

Now, $F_{BC}=\frac{K^{Q^2/4}}{r^2/4}=\frac{{KQ}^2}{r^2}=F$

Then, resultant force according to diagram will be

$F_{resultant}=2F-F=Falong{F}_{A0}$