Answer and Explanation:
According to the question, a metal sphere is hung by a nylon thread and this sphere is uncharged.
Now, in the first case, when positively charged rod is held closer to this sphere the charging of the sphere takes place by induction.
Positively charged rod near to the sphere induces negative charges on the surface of the sphere whereas the positive charges are repelled to the far surface of the sphere.
Now, when the distance between the rod and sphere reduces, force of attraction between both increases.
At the instant, when rod comes in contact with the sphere, charging of sphere takes [place by the method of conduction.
In conduction, same nature of charge is transferred to the object in contact, here positive charge from rod to sphere in same amount.
Since, both the rod and sphere are positively charged they repel.