Question:
The excess pressure inside a soap bubble A is twice that in another soap bubble B. The ratio of volumes of A and B is
The excess pressure inside a soap bubble A is twice that in another soap bubble B. The ratio of volumes of A and B is
Updated On: Nov 8, 2023
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The Correct Option is C
Solution and Explanation
Excess pressure inside the bubble is $ p=\frac{4T}{r} $ Here, $ {{p}_{A}}=2{{p}_{B}} $ $ \frac{{{p}_{A}}}{{{p}_{B}}}=\frac{{{r}_{B}}}{{{r}_{A}}} $ So, radius of bubble $ B $ is $ {{r}_{B}}=2 $ Ratio of volumes $ \frac{{{V}_{A}}}{{{V}_{B}}}={{\left( \frac{{{r}_{A}}}{{{r}_{B}}} \right)}^{3}}={{\left( \frac{1}{2} \right)}^{3}} $ $ \frac{{{V}_{A}}}{{{V}_{B}}}=\frac{1}{8} $
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Concepts Used:
Surface Tension
The amount of energy required to increase the liquid's surface area by one unit area is known as surface tension. In other words, it is a property of the liquid surface to resist force.
Surface tension is defined as,
The ratio of the surface force F to the length L along which the force acts.
Mathematically, the surface tension formula can be expressed as follows:
T=F/L
Where,
- F is the force per unit length
- L is the length in which force act
- T is the surface tension of the liquid
Read More: Detergents and Surface Tension
Factors affecting surface tension:
- Impurities: The surface tension decreases with the addition of impurities.
- Surfactants: Adding surfactants in liquids lowers the tension of water making it interrupt aside or get susceptible.
- Temperature: The surface tension of a liquid reduces as the temperature rises.
The Unit of Surface Tension:
The SI unit of Surface Tension is Newton per Meter or N/m.