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# Dimensions of Surface Tension     ## What is the Dimensional Formula of Surface Tension?

Last updated date: 14th Mar 2023
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Surface tension is the property of any fluid which attempts to minimize its free surface area. The surface tension of a liquid is measured as the force per length acting on an imaginary line drawn tangentially on the liquid's free surface.

Surface tension S = Force/Length which is equal to F/l  in turn equal to  work done/Change in area

SI unit: Nm-1 or Jm-2 and its dimension formula for surface tension is [MT-2].

The quantity is scalar. Surface tension is a molecular phenomenon that is electrical in nature due to cohesive force, and the root cause of force.

The surface tension of a liquid depends only on the nature of the liquid and is independent of the film surface or line length

Small drops in the liquid are spherical due to the surface tension properties.

The force of attraction that acts between the molecules of different substances is called adhesive force, e.g. the force of attraction that acts between paper and ink molecules, water and glass, etc.

### Cohesive Force

The force of attraction acting between the same substance molecules is called a unified force. For example, the force of attraction between water molecules, glass molecules, etc.

### Both Cohesive and Adhesive Forces are Van Der Waals’ Forces.

Surface tension is a tendency of the liquid surfaces to shrink to the minimum possible surface area. The surface tension has the force dimension per unit length or the energy dimension per unit area.

### Dimensional Formula of Surface Tension

The surface tension dimensional formula is given by,

M¹L⁰T⁻²

Where,

• M = Mass

• L = Length

• T = Time

### Derivation

Surface Tension (T) = Force × Length-1 . . . . . (1)

Since, Force = Mass × Acceleration

And, acceleration = velocity × time-1 = [L T-2]

∴ Dimensional unit of surface tension =  M1 L1 T-2 . . . . (2)

Substitute equation (2) in equation (1), later we get,

Surface Tension (T) = Force × Length-1

Or, T = [M1 L1 T-2] × [L-1] = M1 T-2.

Therefore, the surface tension dimension formula is represented as M1 T-2.

## FAQs on Dimensions of Surface Tension

1. What is Surface Tension? State its Formula.

Surface tension of a liquid is referred to as the free surface energy which is inherent in all liquids. This surface tension gives rise to forces which, for example, helps water insects to walk on the surface of the water without sinking due to the gravitational forces balancing the weight of the insect on the surface.  Surface tension is defined as the ratio of surface force F applied to a liquid and the length d over which the force acts. Walking on water is up to the birds, like "floating" a paperclip.

The equation is written as: Surface tension = (surface force)/(length force acts)

2. What is the SI Unit of Tension?

Surface tension is the property of the liquid when at rest in which the surface of the water acts as a membrane which helps balance the weight of the objects if placed right.  The molecules on the water surface can easily break apart if rigorous movements take place on the surface. The force per unit length is the surface tension, perpendicular to a line drawn in the liquid surface. Its SI unit is newtons per metre, with dynes per centimetre being its CGS unit. It has dimensions of MT−2

3. Is Tension a Uniform?

This means the tension in the more vertical part of the rope has to be greater. If the ruler has uniform mass (mass acts in the center), and the rope is light and inextensible, then yes, throughout the tension is equal. The tension force is transmitted through a string, wire, rope or cable pulled tight from either ends by forces acting from opposite ends. It is directed along the length of the rope and pulls equally on the objects on the opposite end.

4. What happens if the surface tension breaks?

The surface tension can be broken only through agitated movement while placing the object denser than water since the balance is disrupted. For example, if we place a small needle on the surface of the water, we are sure that the needle will sink. But if placed carefully, it will float. This happens as long as the object does not disrupt or break through and separate the molecules of the water molecules. Since the outermost layer of water forms the surface, they must compensate to create a stronger bond between the molecules of water which creates the surface tension.

5. What are the different examples of surface tension?

Surface tension is caused when the outermost layer of water comprises molecules having a stronger bond since they are fewer in number. Some of the examples of surface tension are as follows:

• Floating a needle, which is denser than water, on the water surface

• Many tents are made of waterproof material which causes the raindrops to slip out but if the water tension is broken, it will seep through

• Surface tension disinfectants, which when sprayed, floats on the water surface to kill the bacteria

• Soaps and detergents for cleaning clothes that soak through the pores

• Using cold water for washing when the detergent lowers the surface tension