The rod she chooses, to give the sphere a uniform negative charge by induction is the positively charged rod.
Charging an object by induction is a process of inducing a charge on the object by bringing another charged object close to it.
When a positively charged rod is brought near a neutral sphere (equal negative and positive charge), the positive charge of the rod will repel the positive charge of the sphere, leaving the sphere with excess negative charge.
Thus, the rod she chooses, to give the sphere a uniform negative charge by induction is the positively charged rod.
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