A rod is brought near an uncharged pith ball electroscope. What conclusion would you draw about the charge on the rod if the pith ball does not move ?

The pith-ball electroscope is used to detect the presence of a static electricity charge. The two lightweight 'pith' balls suspended from the strings are attracted to objects with a static electric charge. The pith balls can also be charged by touching them to an object with a static electric charge.
The pith-ball electroscope is also useful for detecting electric charges and for determining the polarity of an unknown charge. 
If we bring a non-charged object near a non-charged pith ball electroscope, the pith ball will not move. But if the object is charged, then the pith ball will move towards or away from the charged body because it is attracted to or repelled from it. The attraction prevails until they touch, then they will repel.
In this case, the pith ball does not move.
Hence, the body is uncharged.