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#1223
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Almost. Mine is slightly different.

Added 1 minute ago
Ment
mg=integrate (h from 0 to H) ρg(H-h)*(-sin(α))*dS(h) ----------- (1) It seems like there should be a minus sign here.
Why the minus sign? Which direction are you pointing the axis onto which you are projecting the forces acting on the sphere: up or down?
Всё не так плохо как Вы думаете. Всё намного хуже!