Rule to determine when to use the prefix "im" vs. "un" to negate a word starting with "p"? [duplicate]

I believe that the following other question will help you: Are there any patterns to observe in choosing the correct negative prefix to use?.

In short, it shouldn't matter what letter a word starts with. What matters is where the word came from--its origin affects its proper negation. As the accepted answer (posted by Daniel) said,

In general, words take un- when they are of English (Germanic) origin and in- if they come from Latin. (The forms im-, il-, and ir- are variations on in-.) Apart from that, there’s really no good guide to which one you should choose.

Simchona linked a good reference, but I do see a small difference in the examples you listed.

Polluted, polished, and plugged are all results of physical actions. Plausible, possible, and perfect are all conditions, or adjectives. It makes sense to me that they would be negated differently.

Done - Undone
Spent - Unspent
Paid - Unpaid
Pinned - Unpinned
Hinged - Unhinged

Proper - Improper
Movable - Immovable
Balanced - Imbalanced
Material - Immaterial
Measurable - Immeasurable