The Proto-Indo-European *bhag- "to share out" (IEW 1. bhag- 107) became ancient Greek φαγεῖν phagein "to eat" (ie "to have a share of food").
sarcophagus is from ancient Greek σάρξ sarks "flesh" and phagein - in other words, "flesh eater". sarcasm is from the Greek σαρκάζω sarkazō "to tear flesh like dogs". sarks is from PIE *twerḱ- "to cut".
In Sanskrit the root became भग bhaga "dispenser, gracious lord, patron (applied to gods), good fortune", perhaps something to do with the idea of god sharing out good fortune. Sanskrit भगवद्गीता bhagavad gītā, "Krishna's song", is from bhaga and gītā "song" (from PIE *geh₁i- "to sing").