sou
Synonym discussion
Sense: noun/1
All four words can refer to a coin of very small value, but 'sou' (sense 1) is unique in being almost exclusively negative and idiomatic: you say 'not a sou' to mean zero money, not literally one coin. 'Cent' and 'penny' are everyday terms for the smallest denominations in the US and UK, and they too appear in negative phrases ('not a cent', 'not a penny'), but those phrases still feel literal — you could add 'not a single cent'. 'Farthing' is a historical British coin, now only literary, so it patterns like 'sou' in its dated flavour. 'Dime' is a US ten-cent piece and appears in the idiom 'a dime a dozen' (common and cheap), but it does not carry the 'penniless' connotation that 'sou' does. For the emphatic 'completely broke' meaning, 'sou' is the most dramatic choice.
Etymology
English borrowed 'sou' from French in the early 1800s. The French word itself goes back to Latin 'solidus', the name of a late-Roman gold coin. Over time the meaning shifted from a valuable coin to a tiny copper one, and eventually to the idiomatic sense of 'the smallest possible amount of money'.