The dimensions of surface tension are

The correct answer is Nm⁻¹.

Step-by-Step Explanation:

1. Definition of Surface Tension:
Surface tension is a property of liquid surfaces that causes them to behave like a stretched elastic membrane. It is quantitatively defined as the force acting per unit length along an imaginary line drawn on the surface of the liquid.

2. Mathematical Formula:
The formula for surface tension is given by:

$T=\frac{F}{L}$

where:
- $T$ is the surface tension,
- $F$ is the force acting along the surface line, and
- $L$ is the length over which the force acts.

3. Determining the Unit:
To find the unit of surface tension, we substitute the standard SI units for force and length into the formula:
- The SI unit of force ($F$) is the Newton ($\mathrm{N}$).
- The SI unit of length ($L$) is the meter ($\mathrm{m}$).

Therefore, the SI unit of surface tension is:

$\text{Unit of}T=\frac{\mathrm{N}}{\mathrm{m}}={\mathrm{Nm}}^{-1}$

This corresponds to Newton per meter (${\mathrm{Nm}}^{-1}$).

4. Note on Dimensions:
Although the question refers to "dimensions," the options provided are in terms of units. To find the actual physical dimensions of surface tension:
- The dimensional formula of force ($F$) is $\left[{\mathrm{MLT}}^{-2}\right]$.
- The dimensional formula of length ($L$) is $\left[L\right]$.

Substituting these dimensions into our formula gives:

$\left[T\right]=\frac{\left[{\mathrm{MLT}}^{-2}\right]}{\left[L\right]}=\left[{\mathrm{MT}}^{-2}\right]$

which can also be written as $\left[M^1{L}^0{T}^{-2}\right]$.