Question:
On heating water, bubbles being formed at the bottom of the vessel detatch and rise. Take the bubbles to be spheres of radius $R$ and making a circular contact of radius r with the bottom of the vessel. If $r << R$, and the surface tension of water is T, value of r just before bubbles detatch is (density of water is $\rho_{w}$ )
On heating water, bubbles being formed at the bottom of the vessel detatch and rise. Take the bubbles to be spheres of radius $R$ and making a circular contact of radius r with the bottom of the vessel. If $r << R$, and the surface tension of water is T, value of r just before bubbles detatch is (density of water is $\rho_{w}$ )
Updated On: Jul 13, 2024
- $R^{2}\sqrt{\frac{2 \rho_{w}\,g}{3T}}$
- $R^{2}\sqrt{\frac{\rho_{w}\,g}{6T}}$
- $R^{2}\sqrt{\frac{\rho_{w}\,g}{T}}$
- $R^{2}\sqrt{\frac{3\rho_{w}\,g}{T}}$
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The Correct Option is A
Solution and Explanation
When the bubble gets detached,
Buoyant force = force due to surface tension
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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.