Question

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

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

Hint:

Excess pressure in a soap bubble varies inversely with its radius, and volume varies as the cube of the radius.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
For a soap bubble the excess pressure is \(\Delta P=\dfrac{4T}{r}\), so \(\Delta P\propto\dfrac1r\).

Step 2: Find the radius ratio
\(\Delta P_1=3\Delta P_2\) gives \(\dfrac{r_1}{r_2}=\dfrac{\Delta P_2}{\Delta P_1}=\dfrac13\).

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

Final Answer:
The volumes are in the ratio 1 : 27. \[ \boxed{\text{(C) }1:27} \]