Surface tension has the dimensions:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 2011
Detailed Explanation
Surface tension measures the tensile force exerted across a line of unit length on a liquid surface. Dimensional analysis in the force-length-time system directly identifies its formula.
From the definition of surface tension \(T\):
\[ T = \frac{\text{Force}}{\text{Length}} = \frac{[F]}{[L]} = [F L^{-1}] \]
In the \([M, L, T]\) system: \([F] = [M L T^{-2}]\), so:
\[ [T] = \frac{[M L T^{-2}]}{[L]} = [M T^{-2}] \]
Why “F L⁻¹” Is Correct
Surface tension is force per unit length, giving dimensions [F L⁻¹].
Why the Other Options Are Wrong
- B. F: F is the dimension of total force.
- C. F L⁻²: F L⁻² is the dimension of stress or pressure (force per unit area).
- D. F L⁻³: F L⁻³ is the dimension of specific weight (force per unit volume).
Key Point
Surface tension dimensions: [F L⁻¹] in FLT system, or [M T⁻²] in MLT system.
Key Concepts for Students
- SI unit: N/m; CGS unit: dyne/cm.
- Equivalent thermodynamic dimension: energy per unit area [F L L⁻²] = J/m².
- Water has surface tension of approximately 0.073 N/m at 20°C.
Practice more: this is question 52 in Properties of Fluid MCQs – Part 4. Try the whole set and check every answer instantly.