I was thinking if we have a word like mentioned above in the domain name but NO porn/objectionable content in the website, would it be a problem with adsense?
Only AdSense could answer that. Shit and balls are pretty tame 'adult' words to me, but the AdSense pen-pushers might have a different interpretation. They have past form for disabling sites with swimsuit and underwear shots because they interpreted those as being adult content. Safest if you ask them before you put your code on that domain.
Depends: statshit = stats hit or stat shit I can think of a few more examples, but I don't think something like statshit is bannable. Get creative !