A spherical balloon filled with helium has a radius of 0.3 m and a total mass of 0.5 kg. What is the maximum weight of a payload that can be attached to the balloon so that it just begins to rise? (Density of air = 1.2 kg/m³, g = 9.8 m/s²)

Core Concept

The balloon will begin to rise when the buoyant force equals the total weight. The volume of the sphere is (4/3)πr³ = (4/3)π(0.3)³ ≈ 0.1131 m³. Buoyant force = ρ_air × V × g = (1.2 kg/m³)(0.1131 m³)(9.8 m/s²) ≈ 1.33 N. The weight of the balloon itself is mg = 0.5 kg × 9.8 m/s² = 4.9 N. The maximum payload weight is when buoyant force = balloon weight + payload weight, so payload weight = buoyant force - balloon weight = 1.33 N - 4.9 N = -3.57 N. This negative value indicates the balloon won't rise with its current mass. Let me adjust the question parameters.