Why do we say that repulion is a sure test of charge on an object?
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Because when we bring a chargedbody near an uncharged body an opposite charge is induced on the neutral body. And their will an attraction between them. But the given body is uncharged. Therefore,repulsion is a sure test of charge.
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Why do we say that only repulsion is a sure test of charge on a body?
To set the stage, when you charge a body, like a balloon, you can attach it to another solid nonconducting object . This occurs despite the nature of the charge on the balloon. So, if a balloon has a negative charge and is brought near an object, like a wall, the charge on the balloon will induce a positive charge on the wall so it will stick to the wall. That means that the wall's electrons (the negative electrons are farther from the positively charged nucleus of the atom) will be repelled by the negatively charged balloon but the nuclei of the atoms in the wall will remain in their original positions. This means that the wall has an induced charge because the electrons have been repelled by the negatively charged balloon and the balloon would be attracted to the wall. This charge induction would also work if the balloon was positively charged.
If the balloon were brought close to an oppositely charged object it would naturally be attracted. But, from the previous paragraph we have already shown that the attraction could be caused by an induced charge rather than an real opposite charge. So the attraction proves nothing concerning the actual effect of charge.
If you have two objects that have been charged with the same type of charge, positive or negative, the objects will repel each other. This is a statement of the law of charge which says that opposite charges attract and like charges repel. No matter what you try, the result will always be repulsion, so the same charges on two objects which causes repulsion will be a proof of, or a sure test, of the presence of the same charge on the objects. Repulsion never happens when a charge is induced by one charged object acting on another.
Hope this clears up your thinking.
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