Question

A bottle of soap water is grasped by the neck and swings briskly in a vertical circle. Near which portion of the bottle do the bubbles collect

• A. In the middle of the bottle
• B. Near the neck
• C. Uniformly distributed in the bottle
• D. Near the bottom

Answer 1

Answer: (B)

Near the neck

Answer 2

When the bottle of soap water is swung briskly in a vertical circle by its neck, the neck acts as the center of the circular motion. In the rotating frame of reference, all contents within the bottle experience a centrifugal force directed outwards from the center of rotation. The magnitude of this centrifugal force is proportional to the mass of the object ($F_c = mv^2/r$).

Bubbles are essentially gas pockets, which are significantly less dense than the soap water. Therefore, for the same volume, the mass of a bubble is much less than the mass of the soap water. This means that the soap water experiences a greater centrifugal force than the bubbles.

As a result, the denser soap water is pushed more strongly towards the periphery of the circular path (i.e., towards the bottom or outer parts of the bottle, furthest from the neck), while the lighter bubbles are displaced inwards, towards the center of rotation. The center of rotation is where the bottle is grasped, which is its neck. Hence, the bubbles collect near the neck of the bottle.