The pairs of physical quantities that have the same dimensions is (are):

Options

A. Reynolds number and strain
B. Curie and frequency of a light wave
C. Latent heat and gravitational potential
D. Planck's constant and torque

Answer

To determine which pairs of physical quantities have the same dimensions, we need to analyze the dimensions of each quantity mentioned in the question.

### Step-by-Step Solution:

1. **Identify the Physical Quantities**: We have the following pairs to analyze:
- Reynolds number and Strain
- Curie and Frequency of a light wave
- Latent heat and Gravitational potential
- Planck's constant and Torque

2. **Determine the Dimensions**:
- **Reynolds Number**: This is a dimensionless quantity used in fluid mechanics, defined as the ratio of inertial forces to viscous forces. Its dimensions are \( M^0L^0T^0 \) (dimensionless).
- **Strain**: Strain is defined as the ratio of change in length to original length. It is also dimensionless, hence its dimensions are \( M^0L^0T^0 \).

Since both Reynolds number and strain are dimensionless, they have the same dimensions.

3. **Check Other Pairs**:
- **Curie**: This is a unit of radioactivity and has dimensions of \( M^0L^0T^{-1} \) (since it measures decay per unit time).
- **Frequency of a Light Wave**: Frequency is defined as the number of cycles per second, which has dimensions of \( M^0L^0T^{-1} \).
- Since both Curie and frequency have dimensions of \( M^0L^0T^{-1} \), they also have the same dimensions.

- **Latent Heat**: Latent heat is energy per unit mass, which has dimensions of \( M^1L^2T^{-2} \).
- **Gravitational Potential**: Gravitational potential is defined as energy per unit mass, which also has dimensions of \( M^1L^2T^{-2} \).
- Thus, latent heat and gravitational potential have the same dimensions.

- **Planck's Constant**: Planck's constant has dimensions of \( M^1L^2T^{-1} \) (energy multiplied by time).
- **Torque**: Torque is defined as force multiplied by distance, which has dimensions of \( M^1L^2T^{-2} \).
- Therefore, Planck's constant and torque do not have the same dimensions.

4. **Conclusion**: The pairs of physical quantities that have the same dimensions are:
- Reynolds number and Strain
- Curie and Frequency of a light wave
- Latent heat and Gravitational potential

### Final Answer:
The pairs of physical quantities that have the same dimensions are:
1. Reynolds number and Strain
2. Curie and Frequency of a light wave
3. Latent heat and Gravitational potential