In which case is the buoyant force acting on the soap bubble smaller: 1) at the top of the mountain, 2) at its foot?

The buoyant force acting on the soap bubble will be equal to the weight of the air contained in the volume displaced by it.

At the top of a rather high mountain, the air is thinner. That is, its weight, in the same volume, will be less than, for example, at the foot of a mountain.

Consequently, the buoyancy force acting on the bubble will be less at the top of the mountain than at its foot.

However, the behavior of the bubble will not change in this case: it will float in the air, steadily decreasing under the influence of the gravity of the soapy film that forms it.

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