Dimension of surface tension is:

Explanation:

Dimension of Surface Tension

Definition: Surface tension is a physical property of a liquid that causes its surface to behave like a stretched elastic sheet. It arises due to cohesive forces between the liquid molecules, which are more strongly attracted to each other than to the surrounding air molecules. Surface tension is responsible for phenomena such as the formation of water droplets and the ability of some insects to walk on water.

Formula for Surface Tension:

Surface tension (T) is mathematically defined as the force (F) acting per unit length (L) of a liquid surface:

T = F/L

Here,

• F is the force, with a dimensional formula of M × L × T^-2, where:
  • M represents mass
  • L represents length
  • T represents time
• L is the length, with a dimensional formula of L.

Dimensional Analysis:

To find the dimensional formula of surface tension (T), substitute the dimensions of force (F) and length (L) into the formula:

T = F/L

Dimensional formula of T:

[T] = [F]/[L]

Substituting [F] = M × L × T^-2 and [L] = L:

[T] = (M × L × T^-2) / L

Canceling L in the numerator and denominator:

[T] = M × T^-2

Thus, the dimensional formula for surface tension is:

M × T^-2