Which of the following physical quantity has the dimension of [ML²T⁻³]?

The correct option is power.

To find which physical quantity has the dimensional formula $\left[M{L}^2{T}^{-3}\right]$, we can determine the dimensions of each of the given options step-by-step.

First, recall the dimensions of fundamental quantities:
- Mass is represented by $\left[M\right]$
- Length is represented by $\left[L\right]$
- Time is represented by $\left[T\right]$

Let us analyze the dimensions of the given options:

1. Work:
Work is defined as Force multiplied by Displacement.
Work = Force × Displacement
Since Force = Mass × Acceleration, its dimensions are:
$\text{Dimension of Force}=\left[M\right]\times \left[L{T}^{-2}\right]=\left[ML{T}^{-2}\right]$
Therefore, the dimensional formula for Work is:
$\text{Dimension of Work}=\left[ML{T}^{-2}\right]\times \left[L\right]=\left[M{L}^2{T}^{-2}\right]$

2. Power:
Power is defined as the rate of doing work, or Work divided by Time.
Power = Work / Time
Using the dimensions of Work, the dimensional formula for Power is:
$\text{Dimension of Power}=\frac{\left[M{L}^2{T}^{-2}\right]}{\left[T\right]}=\left[M{L}^2{T}^{-3}\right]$

3. Pressure:
Pressure is defined as Force per unit Area.
Pressure = Force / Area
The dimensional formula for Pressure is:
$\text{Dimension of Pressure}=\frac{\left[ML{T}^{-2}\right]}{\left[L^2\right]}=\left[M{L}^{-1}{T}^{-2}\right]$

4. Impulse:
Impulse is defined as Force multiplied by Time.
Impulse = Force × Time
The dimensional formula for Impulse is:
$\text{Dimension of Impulse}=\left[ML{T}^{-2}\right]\times \left[T\right]=\left[ML{T}^{-1}\right]$

By comparing the calculated dimensions with $\left[M{L}^2{T}^{-3}\right]$, we see that it matches the dimensions of power.