Question

The excess pressure inside the first soap bubble of radius \(R_1\) is three times that inside the second soap bubble of radius \(R_2\). The ratio of volumes of the first bubble to second bubble is

• A. \(1:3\)
• B. \(1:6\)
• C. \(1:27\)
• D. \(1:9\)

Hint:

Excess pressure goes as 1/R and volume as R^3.

Answer 1

The Correct Option is C

Step 1: Invert the pressure ratio:
Larger excess pressure means smaller bubble. $\dfrac{R_1}{R_2}=\dfrac{\Delta P_2}{\Delta P_1}=\dfrac13$.

Step 2: Cube:
$\dfrac{V_1}{V_2}=\dfrac13\cdot\dfrac13\cdot\dfrac13=\dfrac1{27}$.

Step 3: Select:
Option (C).

Final Answer:
Radius ratio 1:3 cubes to a volume ratio of 1:27. \[ \boxed{C} \]