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How exactly do these work? It had initially been described as similar to Dust Release, basically atomizing all that touches it, but it often doesn't have this effect when it hits someone. Why?

EX: Obito was able to grab Sasuke and Naruto with GoDama hands without atomizing them.

EX2: Sasuke was able to stop a GoDama with his imperfect Susano'o

Perhaps the user has control over the disintegrating nature of the Truth Seeking Balls. Or alternatively, the user cannot concentrate on disintegrating nature whilst focusing on making and sustaining massive constructs? Besides, the TSB are made up of multiple natures and/or Kekkei Genkais. So I assume that the TSB can be made out of a base set of natures, and then other natures can be added, eg. Yin-Yang Release to nullify ninjutsu

Either way, the Truth Seeking Balls are a funky technique, and Kishi needs to explain just wtf is up with them, though he probably won't.

Sasuke and Naruto were coated in senjutsu when Obito grabbed them and Sasuke's imperfect Susano'o hand was destroyed.

Originally posted by AuraAngel
Sasuke and Naruto were coated in senjutsu when Obito grabbed them and Sasuke's imperfect Susano'o hand was destroyed.

This.

Also, shouldn't have Sakura just been sliced in half when she slumped on. Madara's stick?

You mean when she ran into it? Presumably the parts of her it touched were destroyed. She just has mad healing.

Shouldn't her healing have been rendered ineffective because GoDama negate the effects of Ninjutsu?

While on the staff sure. But off of it there is no reason it wouldn't heal her. It's not like the Edo Tensei where they are held together by ninjutsu.

Also keep in mind that Hiruzen was able to heal the damage done but Obito was in his crazy mode. This could imply that the Godama can only disintegrate something when the user wants to use them that way. This could be supported by Sasuke being able to stand on one, despite only ever channeling senjutsu through his left hand and Chidori.