Question

The SI unit of surface tension is ________.

• A. $Nm^{-1}$
• B. $Nm^{-2}$
• C. $Nm^{2}$
• D. $Nm$
• E. $N$

Hint:

Surface Tension = Force Length.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
Surface tension is a property of a liquid that allows it to resist an external force. It can be defined in two equivalent ways: as the force per unit length, or as the surface energy per unit area. We can derive the SI unit from either definition.
Step 2: Key Formula or Approach
Definition 1: Force per unit length
Surface Tension (\(T\)) is defined as the force (\(F\)) acting perpendicularly on a line of unit length (\(L\)) on the surface of the liquid.
\[ T = \frac{F}{L} \] Definition 2: Energy per unit area
Surface tension can also be defined as the work done (or surface potential energy, \(E\)) required to increase the surface area (\(A\)) of the liquid by a unit amount.
\[ T = \frac{E}{A} \] We will find the units from both definitions.
Step 3: Detailed Explanation
Using Definition 1 (Force/Length):
- The SI unit of force (F) is the Newton (N).
- The SI unit of length (L) is the meter (m).
- Therefore, the SI unit of surface tension is \(\frac{\text{N}}{\text{m}}\), which is written as \(Nm^{-1}\).
This directly matches option (A).
Using Definition 2 (Energy/Area):
- The SI unit of energy (E) or work is the Joule (J).
- The SI unit of area (A) is the square meter (\(m^2\)).
- Therefore, the SI unit of surface tension is \(\frac{\text{J}}{\text{m}^2}\).
- We know that a Joule is the work done by a force of one Newton over a distance of one meter, so \(1 \text{ J} = 1 \text{ Nm}\).
- Substituting this into the unit: \(\frac{\text{J}}{\text{m}^2} = \frac{\text{Nm}}{\text{m}^2} = \frac{\text{N}}{\text{m}} = Nm^{-1}\).
Both definitions give the same SI unit.
Step 4: Final Answer
The SI unit of surface tension is \(Nm^{-1}\).