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If A Suspended Object A Is Attracted To A Charged Object B, Can We Conclude That A Is Charged?
Answer: No, A is not charged.
No. The object can be uncharged, but have molecules with a dipolar moment; that means that in the presence of electric fields, these molecules will change their orientation. This will make that all the parts of the molecules having opposite charges with object B will be closer to B than to A.
Therefore, the attractive force to A will be greater than the repulsive force.
This, however, makes for small attractions. If one imagines an experiment where a considerable force is exerted, i.e. the bodies are strongly attracted to each other, then most likely object A is charged.