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 to second bubble is

• A. \(1:27\)
• B. \(1:18\)
• C. \(1:9\)
• D. \(1:3\)

Hint:

Excess pressure in a soap bubble is 4T/R, so radius is inversely proportional to excess pressure.

Answer 1

The Correct Option is A

Step 1: Radius
From $P = 4T/R$, a three times larger pressure means a three times smaller radius.

Step 2: Volume
$V \propto R^3$ gives $(1/3)^3 = 1/27$.

Step 3: Answer
1:27, option (A).

Final Answer:
Option (A). \[ \boxed{1:27} \]