2018 A/L Physics Past Paper · Question 22 (English Medium)

Answer: (3) Cluster (3)

What the question asks

We want: the cluster that can really happen.

Relevant theory

The excess pressure inside a soap solution bubble.

$\Delta P = \frac{4T}{r}$

Applying it to this question

Each cluster has one big bubble.

One or more small bubbles are joined to it.

Between two joined bubbles there is one shared film.

The pressures on the two sides of a shared film can differ.

That difference decides how much the film curves.

Where three films meet, they meet at 120°.

What to look at in each drawing:

The radii of the bubbles.

Which way each shared film bends.

Whether any bubbles have the same radius.

Reasoning and calculation

The excess pressure in a soap bubble:

$$\Delta p = \frac{4T}{r}$$

A smaller $r$ gives a bigger excess pressure.

So the small bubble pushes the shared film into the big bubble.

Between equal bubbles the pressures are equal. So the film is flat.

Cluster (3): two equal small bubbles.

The film between them is flat.

Each has a film bulging into the big bubble.

So it follows the rule fully.

Why the other options fail

This option says: cluster (1). The film between unequal bubbles is flat.

But the small bubble has the higher pressure. So the film must bulge into the big bubble.

So it is wrong.

This option says: cluster (2). The small bubble only touches the big one from outside.

But joined bubbles must have a shared film between them.

This option says: cluster (4). Three small bubbles touch only at points.

But joined bubbles must have shared films. They must meet at 120°.

This option says: cluster (5). The films bend into the smaller bubbles.

But the smaller bubble has the higher pressure. So each film must bulge into the bigger bubble.

Checks

Does it make sense?

In cluster (3) the two small bubbles are equal. The film between them is flat.

They have a higher pressure than the big bubble. So their films bulge into it.

Both are true at the same time.

Conclusion

The smaller bubble has the higher pressure.

So its film bulges into the bigger bubble.

Between equal bubbles the film is flat.

The answer is option (3).

Explore

A child blows two soap bubbles, a small one and a big one.

Inside a soap bubble the excess pressure is $\frac{4T}{r}$. The small bubble has the higher pressure.

When they join, the small bubble pushes the shared film into the big one.

In a real cluster every film bulges into the bigger bubble. That is cluster (3).