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If the word नर [nara], sometimes represented as नार [nāra] primarly means 'man, human, person' and the word नारक / नरक [nāraka / naraka] means 'hell', 'infernal' and/or 'inhabitant of hell', then where did this meaning come from?
Are these two words related?
And is it possibly because of क [ka] being a particle for inanimate / unconscious agent (inanimate causative)?
The etymology is not entirely certain. The historical linguist Manfred Mayrhofer in his Etymologisches Wörterbuch des Altindoarischen (vol. 1, pg. 37) essentially says (this is paraphrased from German):
nā́raka (often with lóka) is most likely from the vriddhi form of nar- "man"
which perhaps implies that nā́raka is the final place for flawed (?) men, in opposition to the physical lóka. I think this is the best possible interpretation, -ka is a common nominal suffix.
Another one given by Rendich Franco, which I think is less likely:
naraka "man's [nṛ/nar] unhappiness [aka]"
Regardless, I think there is some derivation from nar- "man".
Another hypothesis is a connection with Greek νέρτερος nérteros "infernal" (perhaps untenable due to the initial reconstructed laryngeal) and English north, both from Proto-Indo-European *h₁ner- "under". This is mentioned in An Etymological Glossary to the Old Saxon Heliand by Samuel Berr but it doesn't seem to be the prevailing theory.
Finally, the grammarian Yāska said that naraka is from ni- "down" + ara "going" + -ka nominal suffix. This is not really phonologically sound and so I find this least likely. This also doesn't explain nāraka that well, which the other two account for with ablaut.
This is from Proto-Indo-European *h₂nḗr. Cognates include Ancient Greek ἀνήρ, genitive ᾰ̓νδρός, whence English andro-.
According to hi.wiktionary:
पुराणों और धर्मशास्त्रों आदि के अनुसार वह स्थान जहाँ पापी मनुष्यों की आत्मा पाप का फल भोगने के लिये भेजी जाती है । वह स्थान जहाँ दुष्कर्म करनेवालों की आत्मा दंड देने के लिये रखी जाती है ।
which is translated, by Google Translate, into:
According to Puranas and Dharmashastras etc., the place where the soul of sinful humans is sent to enjoy the consequence of sin. The place where the souls of the perpetrators are kept to pay the penalty.
From en.wikipedia:
Naraka (Sanskrit: नरक) is the Sanskrit word for the underworld; literally, of man.
which could explain the relationship between नर and नरक.
infact, naraka word originates from tamil verb naranku, which means to kill, punish, beat, thrash etc. the route of formation for naraka is:
naranku > narankam > narakam > naraka = the place where sinners were punished / killed.
If *h2ner- has the same stem as Asura in *h2ens-, then, noting that there's a faux schizm between Zoroastrian and younger Vedic descriptions, tending to good or bad respectively, opposite of the Situation for devas, then ... well, two things.
This negative association might be the same as in naraka.
The reconstruction might have to be zero grade *h2n-, leaving -araka to be explained. I'm not sure if the long vowel in naraka immediately denies this.
At the same time a look at nara, Greek aner (next to andros, not to be confused with anthro-, or Andreas the personal name, or anthrapodon "slave"), and other cognates has to be taken critically.
1.
a) There is no internal derivation given in the wiktionary . The cognates alternate between good and bad meanings: Besides Armenian ayri, Old Prussian ..., as far as I can see, it's otherwise mostly positive, e.g. "hero" or literally whatever, viz Albanian njeri. I don't understand these languages, so even if I'd want to challenge the notion that ayri had a negating n- prefix, I really can't.
b) The notion of heros warrants comparison to Norse einherjar. I see no etymology in wiktionary (though I could swear I saw one before); *h2ner- notes: "alternative form, éh₂nōr, and feminine derivation, éh₂neryeh₂, are seen in many Ancient Greek compositions (i.e. -ήνωρ and -άνειρα)." I think that looks good, but I also think the latter gloss looked like energia. All I'm saying is, the Einherjar went to Valhalla when bravely dead after battle, however that works.
c) Comparing German Narr "fool", Narrentum "foolery" (fool + -dom or + -hood?), närrisch, so far unexplained, might be interesting. There's a geminate consonant, but also so far poorly understood umlaut[1]. The alternate stress pattern might be explainable from use as a slur.
d) Given unexplained opposition between alter and other, a contrast to elder might be assumed. Given *h₂neḱ- "to reach, attain" (cf next), Ger nach, especially nachfolgen, I'd suppose follower, with various connotations for the contrast.
2.
a) For -araka I'd simply suppose earth, and hood. With *h2n- it would be literally un-world, or otherworld. But I'm not too sure about that. Sure enough there are a couple other wordplays. Given 1.d) above, and theories about Asura, then old land or second land or something seems hypothetic, but this hinges on -araka and generally on the history of the word
b) Cp *nirvana, Ger nirgendwo.
Ultimately I'm no wiser than the other answers. If the words only share *h2-n- as root, they may be cognate and not related through derivation. The cognancy might be coincidental (2) or not (1). Derivation does however seem likely, and cognancy from an earlier time less so, if no cognated for naraka can be secured. So I'm pretty sure I missed the answer by a couple miles. My basic answer is no, I see no good reason to think so. For all I know, Naraka might be a specific place that became symbolic (cp. symbolic e.g.Timbuktu).
1: Anatoli Liberman (rez.), 2001, Michael Schulte: Probleme der Umlautphonemisierung ... in Alvissmal 10
