Which of the following physical quantities do not have same dimensions ?

Options

A. Pressure and stress
B. tension and surface tension
C. strain and angle
D. energy and work.

Explanation

To determine which physical quantities do not have the same dimensions, we will analyze each option provided in the question.

### Step 1: Analyze Pressure and Stress
- **Pressure (P)** is defined as force (F) per unit area (A):
\[ P = \frac{F}{A} \]
The dimension of force is \( [F] = [M][L][T^{-2}] \) and the dimension of area is \( [A] = [L^2] \).
Thus, the dimension of pressure is:
\[ [P] = \frac{[M][L][T^{-2}]}{[L^2]} = [M][L^{-1}][T^{-2}] \]

- **Stress (σ)** is also defined as force per unit area:
\[ \sigma = \frac{F}{A} \]
Therefore, the dimension of stress is the same as pressure:
\[ [\sigma] = [M][L^{-1}][T^{-2}] \]

**Conclusion**: Pressure and stress have the same dimensions.

### Step 2: Analyze Tension and Surface Tension
- **Tension (T)** is a force, so its dimension is:
\[ [T] = [M][L][T^{-2}] \]

- **Surface Tension (γ)** is defined as force per unit length:
\[ \gamma = \frac{F}{L} \]
Thus, the dimension of surface tension is:
\[ [\gamma] = \frac{[M][L][T^{-2}]}{[L]} = [M][T^{-2}][L^{-1}] \]

**Conclusion**: Tension and surface tension do not have the same dimensions.

### Step 3: Analyze Strain and Angle
- **Strain** is a dimensionless quantity defined as the ratio of change in length to original length:
\[ \text{Strain} = \frac{\Delta L}{L} \]
Therefore, it has no dimensions.

- **Angle** is also a dimensionless quantity, typically measured in radians:
\[ \text{Angle} = \frac{\text{Arc Length}}{\text{Radius}} \]
Thus, it is also dimensionless.

**Conclusion**: Strain and angle have the same dimensions (both are dimensionless).

### Step 4: Analyze Energy and Work
- **Energy (E)** and **Work (W)** are defined as:
\[ W = F \cdot d \]
where \(d\) is displacement. The dimension of work (and energy) is:
\[ [W] = [F][L] = [M][L][T^{-2}][L] = [M][L^2][T^{-2}] \]

**Conclusion**: Energy and work have the same dimensions.

### Final Conclusion
After analyzing all the options, the only pair of physical quantities that do not have the same dimensions is **Tension and Surface Tension**.

### Answer
**The physical quantities that do not have the same dimensions are Tension and Surface Tension.**