Question

Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is:

• A. 4:1
• B. 0.8:1
• C. 8:1
• D. 2:1

Hint:

Smaller soap bubbles have higher internal pressure due to surface tension effects.

Answer 1

The Correct Option is C

Step 1: {Apply Laplace's pressure equation}
\[\Delta P = \frac{4T}{R}\]Step 2: {Relate pressures and radii}
\[\frac{\Delta P_1}{\Delta P_2} = \frac{R_2}{R_1} \Rightarrow R_1 = 2 R_2\]Step 3: {Determine volume ratio}
\[V_1 : V_2 = R_1^3 : R_2^3 = 8:1\]Consequently, the correct answer is 8:1.