Question:
Two glass plates are separated by water. If surface tension of water is $75$ dyne/cm and area of each plate wetted by water is $8\, cm ^{2}$ and the distance between the plates is $0.12 \,mm$, then the force applied to separate the two plates is
Two glass plates are separated by water. If surface tension of water is $75$ dyne/cm and area of each plate wetted by water is $8\, cm ^{2}$ and the distance between the plates is $0.12 \,mm$, then the force applied to separate the two plates is
Updated On: Jun 23, 2023
- $ 10^2$ dyne
- $ 10^4$ dyne
- $10^5$ dyne
- $10^6$ dyne
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The Correct Option is C
Solution and Explanation
The shape of water layer between the two plates is shown in the figure.
Thickness $d$ of the film $=0.12\, mm$
$=0.012\, cm$
Radius $R$ of the cylindrical face $=\frac{d}{2}$
Pressure difference across the surface
$=\frac{T}{R}=\frac{2 T}{d}$
Area of each plate wetted by water $=A$
Force $F$ required to separate the two plates is given by
$F=$ pressure difference $ \times $ area
$=\frac{2 T}{d} A$
Putting the given values, we get
$F=\frac{2 \times 75 \times 8}{0.012}=10^{5} $ dyne
Thickness $d$ of the film $=0.12\, mm$
$=0.012\, cm$
Radius $R$ of the cylindrical face $=\frac{d}{2}$
Pressure difference across the surface
$=\frac{T}{R}=\frac{2 T}{d}$
Area of each plate wetted by water $=A$
Force $F$ required to separate the two plates is given by
$F=$ pressure difference $ \times $ area
$=\frac{2 T}{d} A$
Putting the given values, we get
$F=\frac{2 \times 75 \times 8}{0.012}=10^{5} $ dyne
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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.