Excess pressure inside a soap bubble is (a) Inversely proportional to its radius (b) Directly proportional to its radius (c) Directly proportional to square roots of its radius (d) Independent of its radius

To answer your question about the relationship between excess pressure inside a soap bubble and its radius, the correct choice is (a) Inversely proportional to its radius. Let's break down why this is the case.

Understanding Excess Pressure in Soap Bubbles

Excess pressure in a soap bubble arises due to the surface tension of the liquid film that forms the bubble. A soap bubble consists of two layers of liquid soap, and the pressure inside the bubble is different from the atmospheric pressure outside it. This difference in pressure is what we refer to as excess pressure.

Key Formula

The relationship between excess pressure (ΔP) and the radius (r) of a soap bubble can be expressed using the formula:

ΔP = 4σ/r

In this equation, σ (sigma) represents the surface tension of the soap solution. From this formula, we can see that excess pressure is inversely related to the radius of the bubble.

Explaining the Inverse Relationship

• If the radius of the bubble increases, the term 'r' in the denominator becomes larger. As a result, the excess pressure (ΔP) decreases.
• Conversely, if the radius decreases, the excess pressure increases. This means smaller bubbles experience greater internal pressure compared to larger bubbles.

Real-World Analogy

Think of a balloon. When you inflate a balloon, the pressure inside increases as the volume decreases (for a fixed amount of air). Similarly, in a soap bubble, as the radius gets smaller, the pressure inside must increase to maintain the balance due to the surface tension effects. This is why smaller bubbles tend to pop more easily than larger ones!

Conclusion

In summary, the excess pressure inside a soap bubble is indeed inversely proportional to its radius. This relationship highlights how physical properties like surface tension can dramatically influence the behavior of everyday objects, such as soap bubbles. Understanding these concepts not only helps in solving physics problems but also deepens our appreciation for the science behind common phenomena.