plod

The root plod (also spelled plaud, plaus, plos) comes from Latin plaudere — 'to clap the hands, to strike, to applaud.' Its past participle was plausus, which is where the -plaus- and -plos- spellings come from. (Note: this Latin root has nothing to do with the ordinary English verb plod, 'to walk heavily.')

The most natural offspring is applause and applaud: ad- (to, toward) + plaudere = to clap toward someone, to express approval by striking your hands together. A Roman audience that liked a performance would applaudere. From the same idea comes plaudit — a burst of applause, a piece of praise. When you 'win plaudits,' people are metaphorically clapping for you.

Now the clever turn. If something is plausible, it is, literally, deserving of applause — plaudere + -ible ('worthy of being clapped at'). An argument so well made that the audience would clap. Over time the meaning softened from 'praiseworthy' to merely 'sounding convincing,' even if it might not be true. That faint shadow of doubt is exactly why we now say a plausible excuse — it sounds good, but maybe too good. Add the negative im- and you get implausible: not even worth clapping at, hard to believe.

The second branch is the surprising one, and it runs through the Roman theater. To explode is ex- (out) + plaudere. But it did not originally mean 'to blow up.' In a Roman theater, the audience drove a bad actor off the stage by clapping, jeering, and hooting him out — they 'clapped him out.' Explodere meant 'to chase off the stage with noise.' From 'to reject loudly' the word drifted to 'to be rejected/cast out,' and then, centuries later, to the modern sense: a sudden, violent, noisy bursting outward — the most theatrical exit of all. (We still keep the old sense in 'to explode a myth' = to drive a false idea off the stage.)

Once explode meant 'burst outward,' English built its mirror image with im- (inward): implode, to burst violently inward — a vacuum tube or a building collapsing in on itself. Explosion / implosion are the noun forms (the -plos- spelling preserving Latin plausus), and explosive is the adjective and the noun for the bursting substance.

So the family has one constant idea — a loud striking of the hands — that fans out in two directions: approval (applaud, plaudit, plausible) and bursting noise (explode, implode). The prefix tells you which way the clap is aimed: ad- toward someone in praise, ex- outward in a blast, im- inward in collapse.