Question

What is the dimensional formula of surface tension?

Answer 1

Hint: In order to find the dimensional formula of surface tension, we need to know the formula for surface tension which comprises known variables. Surface tension formula is given as the ratio of force and length. Using this, find the dimensional formula.

Complete Step by Step Solution:
Surface tension is defined as the property of fluids which has the capability to resist an external force due to cohesive force of water molecules. It is also defined as the property of fluid which has the capability to shrink its surface area to the minimal value. Surface tension depends not only on the forces of attraction between the molecules but also the magnitude of the force, the surface comes in contact with.
Surface tension is directly related to the force applied on the surface of the water either by a solid or gas, when it comes in contact with it. Surface tension in a liquid is caused due to the extensive application of Van der Waals forces of attraction between the molecules that pull the molecules together whenever a force is applied on it. Surface unit is measured in \[N/m\]or in CGS units as \[dyne/cm\].
Surface tension can be mathematically calculated as the ratio of magnitude of force and length of the force applied, which is mathematically given as ,
\[ \Rightarrow \gamma = \dfrac{F}{L}\]
Now, we know that force is given as the product of mass and acceleration or It’s SI unit is given as\[Kg - m/{s^2}\]. Using this, we dimensionally get the formula for force as , \[[ML{T^{ - 2}}]\]. Using this in the equation for surface tension we get,
\[ \Rightarrow \gamma = \dfrac{{[ML{T^{ - 2}}]}}{{[L]}}\]
Taking the denominator to the numerator with a power of -1 ,we get,
\[ \Rightarrow \gamma = [M{L^{1 - 1}}{T^{ - 2}}]\]
\[ \Rightarrow \gamma = [M{L^0}{T^{ - 2}}]\]

Thus, the dimensional formula of surface tension is identified and verified using it’s formula.

Note: One of the major applications of surface tension is the capillary action. The surface tension holds the surface of the fluid afloat, when the capillary tube is immersed inside the water, which causes water to form a hemispheric shape on the mouth of the tube.