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

The correct option is: Near the neck.

To understand why the bubbles collect near the neck of the bottle, let us analyze the forces acting on the liquid and the bubbles during the circular motion.

When the bottle of soda water is swung briskly in a vertical circle while being grasped by the neck, it undergoes circular motion. In the frame of reference of the rotating bottle, every particle experiences a centrifugal force acting radially outwards, away from the center of rotation (which is near the neck of the bottle).

The centrifugal force acting on a mass $m$ at a distance $r$ from the axis of rotation with angular velocity $\omega$ is given by:
$F_{\text{cf}}=m{\omega }^{2}r$

Because the density of the carbonated liquid (soda water) is much greater than the density of the carbon dioxide gas bubbles (${\rho }_{\text{liquid}}\gg {\rho }_{\text{bubble}}$), the heavier liquid experiences a much stronger centrifugal force per unit volume than the lighter bubbles.

As a result, the denser liquid is flung outwards toward the bottom of the bottle (which is farthest from the center of rotation, i.e., the neck). The lighter gas bubbles, having much less inertia and being displaced by the denser liquid, are pushed inwards toward the center of rotation.

Since the bottle is held by the neck, the neck represents the region closest to the center of rotation (smallest $r$). Therefore, the bubbles collect near the neck of the bottle.