Which pair of physical quantities has the same dimension?

The fundamental dimensions are Mass ($\text{M}$), Length ($\text{L}$), and Time ($\text{T}$).

• Pressure: Force per unit area.

  • Force ($\text{F}$) = mass $\times$ acceleration = $\text{M} \times \text{LT}^{-2} = \text{MLT}^{-2}$
  • Area ($\text{A}$) = $\text{L}^2$
  • Dimension of Pressure = $\frac{\text{F}}{\text{A}} = \frac{\text{MLT}^{-2}}{\text{L}^2} = \text{ML}^{-1}\text{T}^{-2}$

• Stress: Force per unit area.

  • Dimension of Stress = $\frac{\text{F}}{\text{A}} = \frac{\text{MLT}^{-2}}{\text{L}^2} = \text{ML}^{-1}\text{T}^{-2}$

• Work: Force $\times$ distance.

  • Dimension of Work = $\text{F} \times \text{L} = \text{MLT}^{-2} \times \text{L} = \text{ML}^2\text{T}^{-2}$

• Force: Mass $\times$ acceleration.

  • Dimension of Force = $\text{MLT}^{-2}$

• Velocity: Distance per unit time.

  • Dimension of Velocity = $\frac{\text{L}}{\text{T}} = \text{LT}^{-1}$

• Acceleration: Change in velocity per unit time.

  • Dimension of Acceleration = $\frac{\text{LT}^{-1}}{\text{T}} = \text{LT}^{-2}$

• Length: Fundamental dimension = $\text{L}$

• Mass: Fundamental dimension = $\text{M}$

• A) Pressure and stress: Both have dimensions $\text{ML}^{-1}\text{T}^{-2}$. These are the same.
• B) Work and force: Work has $\text{ML}^2\text{T}^{-2}$, and Force has $\text{MLT}^{-2}$. These are different.
• C) Velocity and acceleration: Velocity has $\text{LT}^{-1}$, and Acceleration has $\text{LT}^{-2}$. These are different.
• D) Length and mass: Length has $\text{L}$, and Mass has $\text{M}$. These are different.

The physical quantities with the same dimension are pressure and stress.

The final answer is $\boxed{\text{A}}$