What is the dimension of surface tension ?

The correct option is [ML⁰T⁻²].

To find the dimension of surface tension, we can start from its fundamental physical definition.
Surface tension is defined as the force per unit length acting perpendicular to an imaginary line drawn on the surface of a liquid.
Mathematically, surface tension ($T$) is represented as:

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

where:
$F$ is the force, and
$L$ is the length.

Now, let's write the dimensional formula for each of these quantities:

1. Dimensional formula of force ($F$):
Since force is mass times acceleration ($F=m·a$), its dimensional formula is:
$\left[F\right]=\left[{\mathrm{MLT}}^{-2}\right]$

2. Dimensional formula of length ($L$):
$\left[L\right]=\left[L\right]$

Substituting these dimensions into the formula for surface tension, we get:

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

Simplifying the expression by cancelling the length dimension ($L$) from the numerator and denominator:

$\left[T\right]=\left[{\mathrm{ML}}^0{T}^{-2}\right]$

Therefore, the dimension of surface tension is [ML⁰T⁻²].