Explain why: a) A balloon filled with helium does not rise in the air indefinitely but halts after a certain height (neglect winds).

Hint: To answer this question, we have to apply the concepts of buoyancy. The relative density of an object compared to the medium in which it is placed decides whether the object will float or sink. A less dense object in a denser medium will float and vice versa.

Complete step by step answer:
The balloon initially rises in the air because the weight of the displaced air i.e., upthrust is greater than the weight of the helium and the balloon. This force is similar to the force experienced when an empty container is dipped in water.
The difference in densities causes the less dense object to be pushed above. Since the density of air decreases with height therefore the balloon halts at a particular height. At this particular point, the density of the air will be equal to the density of the helium inside the balloon.
The force acting on the balloon downwards that is the weight of the balloon will be balanced by the buoyant force acting on the balloon at this particular point. Hence the net force acting on the balloon will be cancelled out and the balloon stops rising.

Note: Here, we can treat the helium inside the balloon as a liquid to apply the principles of buoyancy. Helium is less dense than air at the ground i.e., at atmospheric pressure near the ground so it will rise up. Atmospheric pressure decreases with height as Earth’s gravity gets weaker with increasing height. However, helium balloons are so light that they can be easily displaced by the wind in which case the dominant force will be the wind of the balloon and not buoyant force.