Let us suppose the magnitude of the original Coulomb force between the two charged spheres is F. In this scenario, a third sphere touches the grey sphere and the red sphere multiple times, being grounded each touch. If the grey sphere is touched twice, and the red sphere is touched three times, what is the magnitude of the Coulomb force between the spheres now?

F/32

Explanation:

GIVEN

that the electrostatic force between sphere = F = kQq/r2

ANSWERED

Any time, third sphere touches the red or grey sphere the charges in it, will reduced to half, also, as half the charges are moved into the third sphere. That makes both spheres have equal charges (grounded) .

Also, the 3rd sphere tries to touch the grey sphere two times. Then, when we have initial charge in it to be Q, then, the final charge will be given has Q / (2x2) = Q/4

The similarly with the red sphere, has the initial charge was q, so we have last charge after the third sphere has touches it three times = q/(2x2x2) =q/8

Therefore,given that the new coulombs force = kQq/(r2x4x8) = F/32

the answer would be 32*f