Surface tension represents force acting along a line at a liquid interface. What is the correct dimension of surface tension in terms of force F and length L?

Introduction / Context:
Surface tension appears in capillarity, bubble formation, and atomization. It is physically the force per unit length acting along a line in the surface, or equivalently energy per unit area. Getting its dimensions right is essential for correct use in correlations like Weber number and capillary rise equations.

Given Data / Assumptions:

• Surface tension symbol γ (or σ) with common units N/m (SI).
• Force denoted by F; length by L.
• Alternative energy interpretation: J/m^2 also equals N/m.

Concept / Approach:

By definition, surface tension = force per unit length. Hence its dimensions are force divided by length. This aligns with many interface mechanics derivations and balances at three-phase contact lines.

Step-by-Step Solution:

Verification / Alternative check:

SI unit check: N/m corresponds exactly to the stated dimension. In base dimensions, γ = M T^-2 (since N = M L T^-2, divided by L → M T^-2), which agrees with F L^-1.

Why Other Options Are Wrong:

F^-1·L, F·L^-2, F^-2·L: These do not match the fundamental definition and lead to inconsistent units in capillarity balances.

Common Pitfalls:

Confusing surface tension with pressure (F L^-2) or elastic modulus; mixing up with interfacial energy units without the area relation.

Final Answer:

F L^-1