Select the pair whose dimensions are same

Options

A. pressure and stress
B. stress and strain
C. pressure and force
D. power and force

Explanation

To solve the question of selecting the pair whose dimensions are the same, we will analyze the dimensions of each pair provided in the options.

### Step-by-Step Solution:

1. **Understanding Dimensions**:
- Dimensions of a physical quantity are expressed in terms of fundamental quantities (mass, length, time, etc.).

2. **Option A: Pressure and Stress**:
- **Pressure**: Defined as force per unit area.
\[ \text{Pressure} = \frac{\text{Force}}{\text{Area}} = \frac{F}{A} \]
The dimension of force (F) is \( [M^1 L^1 T^{-2}] \) and the dimension of area (A) is \( [L^2] \).
\[ \text{Dimension of Pressure} = \frac{[M^1 L^1 T^{-2}]}{[L^2]} = [M^1 L^{-1} T^{-2}] \]

- **Stress**: Also defined as force per unit area.
\[ \text{Stress} = \frac{\text{Force}}{\text{Area}} = \frac{F}{A} \]
Thus, the dimension of stress is the same as pressure:
\[ \text{Dimension of Stress} = [M^1 L^{-1} T^{-2}] \]

- **Conclusion for Option A**: Both pressure and stress have the same dimensions.

3. **Option B: Stress and Strain**:
- **Strain**: Defined as the ratio of change in length to original length, which is dimensionless.
- **Conclusion for Option B**: Stress has dimensions \( [M^1 L^{-1} T^{-2}] \) while strain is dimensionless. Therefore, they do not have the same dimensions.

4. **Option C: Pressure and Force**:
- **Force**: The dimension of force is \( [M^1 L^1 T^{-2}] \).
- **Conclusion for Option C**: Pressure has dimensions \( [M^1 L^{-1} T^{-2}] \) and force has dimensions \( [M^1 L^1 T^{-2}] \). They do not have the same dimensions.

5. **Option D: Power and Force**:
- **Power**: Defined as work done per unit time.
\[ \text{Power} = \frac{W}{T} = \frac{F \cdot S}{T} \]
Where work (W) is force times distance (F·S). Thus, the dimension of power is:
\[ \text{Dimension of Power} = \frac{[M^1 L^1 T^{-2}] \cdot [L^1]}{[T^1]} = [M^1 L^2 T^{-3}] \]
- **Conclusion for Option D**: Force has dimensions \( [M^1 L^1 T^{-2}] \) while power has dimensions \( [M^1 L^2 T^{-3}] \). They do not have the same dimensions.

### Final Conclusion:
The only pair with the same dimensions is **Option A: Pressure and Stress**.