Question

why does a plastic ruler that has been rubbed with a cloth have the ability to pick up small pieces of paper

Answer 1

The ruler will have a static charge.

Suppose the ruler is charged positively.

When brought near a small piece of paper, the piece of paper nearest will acquire a negative charge and the opposite end of the paper will have a positive charge (a separation of charges occurs within the paper).

This would cause an attraction between the ruler and the paper.