1. The problem statement, all variables and given/known data A helium balloon of mass 0.2kg and volume 1m3 is attached to a long thin rope of mass density 1g/m. The coils of rope lay flat on the ground, so that as the balloon moves up the rope unwinds without resistance. How high will the balloon rise? Air density = 1.204kg/m3 a) 1204m b) 1004m c) 602m d) 502m e) none of the above 2. Relevant equations P = pgh 3. The attempt at a solution I think the balloon will stop rising when the pressure inside the balloon equals the pressure of the air on the outside. Pressure of balloon: P(balloon) = F/A V = 4/3πr3 --> r = 0.6204m SA = 4πr2 --> A = 4.835m2 P(balloon) = F/A = 0.4053N/m2 P(balloon)=P(air) P(balloon)=ρairgh 0.4053 = (1204)(9.8)h h=0.0000343m This answer is clearly wrong... Not sure where I'm going wrong.