Question:
A vessel, whose bottom has round holes with diameter $0.1\, m\, m$, is filled with water. The maximum height up to which water can be filled without leakage is
(Surface tension of water $= 75$ dyne $cm^{-1}$ and $g = 1000\, cm\,s^{-2}$)
A vessel, whose bottom has round holes with diameter $0.1\, m\, m$, is filled with water. The maximum height up to which water can be filled without leakage is
(Surface tension of water $= 75$ dyne $cm^{-1}$ and $g = 1000\, cm\,s^{-2}$)
Updated On: Nov 27, 2024
- $100\,cm$
- $75\,cm$
- $60\,cm$
- $30\,cm$
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The Correct Option is D
Solution and Explanation
As $\frac{2T}{R}=\rho gh$,
$h=\frac{2T}{R\rho g}=\frac{4T}{D\rho g}$
$=\frac{4\times75}{0.1\times10^{-1}\times10^{3}}$
($\because R=D/2$ and $\rho=1g/$per $cc$)
or $h=30\,cm$
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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.