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The property of any fluid that attempts to minimize its free surface area is known as surface tension. The Force per length acting on an imaginary line drawn tangentially on the free surface of a liquid is used to calculate its surface tension. Surface tension S = Force/Length, equal to F/l, equal to work done/area change. The SI unit is Nm-1 or Jm-2, and the dimensional formula of surface tension is [MT-2]. The quantity is a scalar value. Surface tension is a molecular phenomenon that is electrical and is the root cause of Force. The surface tension of a liquid is determined solely by its composition and is unaffected by the film surface or line length. Because of the surface tension properties of the liquid, small drops are spherical. The concept of Surface tension and its dimension is an important topic for JEE Preparation.
Surface Tension is a physical property of liquids that describes the force acting on the surface of a liquid, which causes it to behave like a stretched elastic sheet. This property is due to the attractive forces between the molecules at the surface of the liquid. Surface tension is responsible for phenomena such as water droplets forming spherical shapes and insects walking on water.
Surface Tension Definition
Surface tension can be defined as the force per unit length acting along the surface of a liquid. It is represented by the symbol γ (gamma) and is measured in terms of force per unit length, usually in newtons per meter (N/m).
Mathematically, surface tension is expressed as:
Surface Tension (γ) = Force (F) / Length (L)
Dimensional Formula of Surface Tension
The dimensional formula is an expression that shows how and in what combination the fundamental quantities (mass, length, time, etc.) contribute to a given physical quantity.
To find the dimensional formula of surface tension, we need to express it in terms of its fundamental quantities.
Since surface tension is the ratio of force to length, we start with the dimensional formula for force. According to Newton’s second law, Force (F) is given by:
F = ma
Where:
- m = mass
- a = acceleration
The dimensional formula of force is derived as:
Dimensional Formula of Force (F) = [M L T-2]
Now, surface tension is force per unit length:
Surface Tension = Force (F) / Length (L)
So, the dimensional formula of surface tension is:
Dimensional Formula of Surface Tension (γ) = [M L T-2] / [L] = [M T-2]
Thus, the dimensional formula of surface tension is:
[M T-2]
Explanation of Dimensional Formula
- M represents mass.
- L represents length.
- T represents time.
In the dimensional formula [M T-2], there is no length (L) term because it gets canceled out when force is divided by length. The formula indicates that surface tension depends on mass and time but not directly on length.
Units of Surface Tension
The SI unit of surface tension is newtons per meter (N/m). It can also be expressed in terms of energy per unit area, such as joules per square meter (J/m²), since 1 N/m is equivalent to 1 J/m².
Conclusion
Surface tension plays an important role in everyday phenomena, especially involving liquids. Understanding its dimensional formula [M T-2] helps us grasp how surface tension is related to other physical quantities like mass and time.
