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
Show Hint
- 5:3
- 3:2
- 2:3
- 1:1
- 3:5
The Correct Option is B
Solution and Explanation
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).
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