Question

The excess pressure inside the first soap bubble is three times that inside the second soap bubble. The ratio of volume of the first to that of the second bubble is

• A. 1:27
• B. 9:1
• C. 1:9
• D. 1:3

Hint:

Excess pressure is inversely proportional to the radius, and volume goes as the cube of the radius.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
For a soap bubble, the excess pressure is \(\Delta P=\dfrac{4T}{r}\), so \(\Delta P\propto\dfrac{1}{r}\).

Step 2: Radius ratio
\(\dfrac{\Delta P_1}{\Delta P_2}=3\), so \(\dfrac{r_1}{r_2}=\dfrac{1}{3}\).

Step 3: Volume ratio
\(\dfrac{V_1}{V_2}=\left(\dfrac{r_1}{r_2}\right)^3=\dfrac{1}{27}\).

Final Answer:
The ratio of the volumes is 1:27. \[ \boxed{\text{(A) }1:27} \]