Units And Measurement

The surface tension of a liquid is defined as the force per unit length in the plane of the liquid surface, acting at right angles on either side of an imaginary line drawn in the surface.


Hence, dimensions of surface tension are .
Alternative : Surface tension of a liquid is equal to the work required to increase the surface area of the liquid film by unity at constant temperature.

Hence, dimensions of surface tension are

Put the dimensions for each physical quantity in the given relation. Given,

Squaring the equation on either side, we have


Putting the dimensions of equations on RHS,
we get
being a number is dimensionless, we have