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Correct option is D)

$Step 1: Calculation of initial force$

Let $B$ and $C$ have charge $Q$ each initially and are seperated by $r$ distance.

From Coulomb's law, force between them $F=r_{2}KQ_{2} $ $....(1)$

$Step 2: Distribution of charges$

When an identical uncharged spherical conductor $A$ is brought in contact with charged sphere $B$.

By symmetry, the total charge will be shared equally among them, as both have equal radii.

$∴$ Charge on $A$ and $B$ $=2Q $

Now, when the conductor $A$ is brought in contact with $C$.

They will also share equal charge among themselves, as both have equal radii.

$∴$ Charge on $A$ and $C$ $=2Q+2Q =43Q $

$Step 3: Calculation of new force$

New coulomb force between $B$ and $C$:

$F_{′}=r_{2}K2Q ×43Q =83 r_{2}KQ_{2} $

From equation $(1)$, we get: $F_{′}=83 F$

Hence, Option D is correct

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