Whether it is possible to consider the balloon a material point when determining buoyancy force of FA operating on a sphere in air? You receive the answer here.
We apply Archimedes's law
According to Archimedes's law, the balloon which is airborne is affected by the pushing-out Fa force equal ρgV (Fa = ρgV) where: ρ is the density of air; g is acceleration of gravity, V is a volume.
But, you should not forget that the balloon having the mass of m is influenced by Ft gravity = mg forcing our sphere to move vertically down with a speed of free fall.
If the pushing-out force of Fa is more than the gravity of Ft, then the sum of all forces operating on a sphere (net force) will be other than zero and is directed up, and our sphere will fly up.
To increase Fa and to reduce Ft, it is necessary to increase the volume of V and it is desirable to reduce the mass of m of our sphere. Will lead decrease in density of air which filled the flying unit to decrease in mass of the balloon. Decrease in density of air can be reached by its heating or as option, fillings of a cavity of a sphere with light gas, for example, hydrogen.
Balloon as material point
Let's consider the balloon as a material point. But the material point has no volume, having only the weight as its physical characteristics are not measurable.
Leaves these reasonings that the volume of our sphere in the form of a point is equal to 0. At calculation of the carrying (pushing-out) Fa power we will see that it is also equal to zero. At the same time, the mass of a sphere of m, so and force of influence of weight of Ft directed down will not get to anywhere.
Thus, representing our sphere a material point, we exclude impact on it of the carrying power of Fa that contradicts a practical side of a question.
In other words, a point as a body which sizes can be neglected the sphere cannot be owing to the fact that such physical quantities as the volume and weight are necessary for us for determination of its density.
Let's formulate the answer to a question: when calculating Archimedes force the sphere which is airborne a material point cannot be.