# Dimensions of Surface Tension

Introduction: What is the Dimensional Formula of Surface Tension?

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 attracts that act 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] = MT-2.

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

1. What is Surface Tension? State its Formula.

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 paper clip.

The equation is written as:

Surface tension = (surface force)/(length force acts)

2. What is the SI Unit of Tension?

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.