A plastic rod is charged up by rubbing a wool cloth, and brought to an initially neutral metallic sphere that is insulated from ground. It is allowed to touch the sphere for a few seconds, and then is separated from the sphere by a small distance. After the rod is separated, the rod:

A) is repelled by the sphere.

B) is attracted to the sphere.

C) feels no force due to the sphere.

I know the answer is A, but I don't understand why. how do we know that the sphere and the rod have the same charge? What does it mean to be insulated from the ground?

Yes option A is right.

Explanation:

As we know that the "Opposite charges attract and like charges repel eachother". So based upon that fact we find out the sphere will be repelled or attract by the rod. As in this case metallic sphere was neutral initially but then we touched the rod with it. Although it was for few seconds but the charge is transferred to the sphere. Now both sphere and the rod have charge. After the seperation we look towards their respond If both have the opposite charge they will attract eachother. But here in this case they repel because they have the same charge, as we have charged the neutral sphere with the rod so we already know that they have the same charges that is why they are repelling eachother.

       Insulation from the ground means that blocking the way of charges or free electrons from earth to metallic sphere and vice versa. As there exists free electrons and charges in earth they would flow into the metallic objects. So for more precise and accurate experiments we insulate the metals or prevent the metals from touching the earth surface to avoid the flow of charges through  them. I hope it will help you.

i think they are all correct

explanation:

they seem good