Question

The dimensions of surface tension in terms of fundamental quantities energy [E], velocity [v] and time [T] will be-
1. [E⁰v-1T1]
2. [E¹v-2T-2]
3. [E²v-2T-2]
4. [E⁰v-2T-3]

Answer 1

Correct Answer - Option 2 : [E¹v-2T-2]

The correct answer is option 2) i.e. [E1v-2T-2]

CONCEPT:

• Surface tension: Surface tension is a measure of the cohesive forces between liquid molecules present at the surface.​
• Molecules at the surface of a liquid are partly exposed to the surrounding. The molecules at the liquid-air interface experience fewer interactions and have more energy to escape to the surrounding.
• Therefore, energy is required to bring molecules from the bulk of the liquid to the surface. The stronger the intermolecular interaction, the greater is the energy required to increase the surface area of a liquid.

This energy is called surface energy and is related to surface tension as:

​Surface tension, F = \(\frac{ surface \:energy}{area}\)

EXPLANATION:

• Area = length × length = (length)² = (velocity × time)²
• Thus, dimension of area = [vT]²
• Dimension of surface energy = [E]
• Dimensions of surface tension = \(\frac{[E]}{[vT]^2} = [E^1v^{-2}T^{-2}]\)