The balloon Case:
A balloon rises when immersed in a fluid if the net upward force on the balloon due to the fluid it is immersed in (the buoyancy) is greater than the weight of the balloon. Archimedes’ principle states that the buoyancy is equal to the weight of the fluid displaced by the balloon.
Let’s consider the gas in the balloon as helium. The helium balloon displaces a volume of air, that here, clearly, has a greater mass than the mass of balloon, and the mass of the helium gas it contains. Helium has a molecular mass approximately 7 times less than that of air. Because the helium balloon displaces a volume of air that has a greater mass than the mass of the filled balloon, there is a net buoyant force on the balloon that causes the balloon to rise.
The Rocket Case:
The propulsion of rockets is explained by the principle of Newton’s third law of motion. Matter is forcefully ejected from a system, producing an equal and opposite reaction on what remains. A rocket in its simplest form is a chamber enclosing a gas under pressure. A small opening at one end of the chamber allows the gas to escape, and in doing so provides a thrust that propels the rocket in the opposite direction.