Pairs of physical quantities having same dimensions are

Options

A. Reynolds number and strain
B. Torque and force
C. Curie and frequency
D. Gravitational potential and latent heat

Explanation

To solve the problem of identifying pairs of physical quantities that have the same dimensions, we will analyze each option provided in the question.

### Step-by-Step Solution:

1. **Understanding Dimensions**:
- The dimensions of a physical quantity are expressed in terms of mass (M), length (L), and time (T). For example, the dimension of force is [F] = MLT⁻².

2. **Option 1: Reynolds number and Strain**:
- **Reynolds Number**: This is a dimensionless quantity, represented as [Re] = M⁰L⁰T⁰.
- **Strain**: Strain is also dimensionless, represented as [Strain] = M⁰L⁰T⁰.
- **Conclusion**: Both have the same dimensions (dimensionless). Therefore, this option is correct.

3. **Option 2: Torque and Force**:
- **Torque**: Torque is defined as the product of force and distance (Torque = r × F). Its dimensions are [Torque] = MLT⁻² × L = ML²T⁻².
- **Force**: The dimensions of force are [Force] = MLT⁻².
- **Conclusion**: The dimensions of torque and force are different. Therefore, this option is incorrect.

4. **Option 3: Curie and Frequency**:
- **Curie**: Curie is a unit of radioactivity, defined as disintegrations per second. Its dimensions are [Curie] = T⁻¹.
- **Frequency**: Frequency is defined as the number of occurrences of a repeating event per unit time, also having dimensions [Frequency] = T⁻¹.
- **Conclusion**: Both have the same dimensions. Therefore, this option is correct.

5. **Option 4: Gravitational Potential and Latent Heat**:
- **Gravitational Potential**: The gravitational potential energy per unit mass is given by [Gravitational Potential] = MLT⁻² / M = LT⁻².
- **Latent Heat**: Latent heat is defined as the heat required to change the state of a substance without changing its temperature, which also has dimensions of energy per unit mass, hence [Latent Heat] = MLT⁻² / M = LT⁻².
- **Conclusion**: Both have the same dimensions. Therefore, this option is correct.

### Final Answer:
The pairs of physical quantities having the same dimensions are:
- Option 1: Reynolds number and Strain (Correct)
- Option 3: Curie and Frequency (Correct)
- Option 4: Gravitational Potential and Latent Heat (Correct)

Thus, the correct options are 1, 3, and 4.