A balloon whose volume is 300m3 is filled with hydrogen. If the density of air is 1.3 kgm-3, find the upthrust on the balloon. [g = 10$ms^{-2}$]

Analyze the question The balloon is surrounded by air, so the upthrust on it is the weight of the air it displaces (Archimedes' principle, which also applies to gases).

Concept Upthrust = weight of fluid displaced = ρ × V × g

Here the fluid is air, and the volume displaced equals the volume of the balloon.

Solution

• Volume of air displaced, V = 300 m³
• Density of air, ρ = 1.3 kg/m³
• g = 10 m/s²

Mass of air displaced = ρV = 1.3 × 300 = 390 kg

Upthrust = mg = 390 × 10 = 3900 N

The density of hydrogen is not given, and it isn't needed. It would matter only if you were asked for the net lifting force (upthrust minus the weight of the hydrogen and the balloon). The question asks only for the upthrust.

Tip Upthrust depends on the density of the fluid outside the object, not on what is inside it. For any "find the upthrust" question, use ρ(fluid) × V(submerged or displaced) × g. Don't let extra details like "filled with hydrogen" distract you.