Question

If the radii of two soap bubbles are respectively 2 cm and 3 cm, then the ratio of the excess pressures inside the soap bubbles is

• A. 5:3
• B. 3:2
• C. 2:3
• D. 1:1
• E. 3:5

Hint:

The excess pressure in a soap bubble is inversely proportional to its radius. Use the formula \( \Delta P = \frac{4 \sigma}{r} \) to find the pressure ratio.

Answer 1

The Correct Option is B

The excess pressure inside a soap bubble is given by the formula: \[ \Delta P = \frac{4 \sigma}{r} \] 
where: 
- \( \Delta P \) is the excess pressure, 
- \( \sigma \) is the surface tension of the soap film, 
- \( r \) is the radius of the bubble. Let \( r_1 = 2 \, {cm} \) and \( r_2 = 3 \, {cm} \) be the radii of the two bubbles. 
The ratio of the excess pressures is: \[ \frac{\Delta P_1}{\Delta P_2} = \frac{\frac{4 \sigma}{r_1}}{\frac{4 \sigma}{r_2}} = \frac{r_2}{r_1} \] 
Substituting the given values: \[ \frac{\Delta P_1}{\Delta P_2} = \frac{3}{2} \] 
Thus, the ratio of the excess pressures is 3:2. 
Therefore, the correct answer is (B).