Question

Why does a hot air balloon float?

Answer 1

The most accurate answer among the choices would be the fourth one, because if the weight of the air displaced is greater than the balloon's weight, the balloon will float upwards. Density of the air also plays a part. Hot air = less dense. Hope my answer has come to your help.

Answer 2

Right answer: The weight of the air displaced is less than the volume of the balloon

A hot air balloon is a cloth wrap that contains several thousand cubic meters of air inside (a large volume of air). The burner (which is the motor of the balloon and responsible for its elevation) heats the liquid propane to a gaseous state to generate a huge flame, thus heating the air mass inside the balloon. In this way, its density is modified with respect to the air that surrounds it, because the hot air is lighter than the outside air (less dense), causing the balloon to rise and float.

Now, if we know that the density of a body $d$ is directly proportional to its mass $m$ and inversely proportional to its volume $V$:

$d=\frac{m}{V}$

We can deduce that

by increasing the volume of the body, its density will decrease.

This is proof of Archimedes' Principle:  

A body totally or partially immersed in a fluid at rest, experiences a vertical upward thrust equal to the mass weight of the body volume that is displaced.

In this case the fluid is the air outside. So, the warm air inside the balloon, being less dense, will weigh less than the outside air and therefore will receive an upward pushing force or thrust that will make the balloon ascend.