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

Options

A. Reyaold number and coefficient of friction
B. Curie and frequency of a light wave
C. Latent beat and gravitational potential
D. Planck's constant and torque

Explanation

To solve the question regarding the pairs of physical quantities that have the same dimensions, we will analyze each pair one by one.

### Step 1: Analyze Reynolds Number and Coefficient of Friction
- **Reynolds Number (Re)**: It is a dimensionless quantity, defined as the ratio of inertial forces to viscous forces. Its dimensions are \( M^0 L^0 T^0 \).
- **Coefficient of Friction (μ)**: It is also a dimensionless quantity, defined as the ratio of the force of friction to the normal force. Its dimensions are also \( M^0 L^0 T^0 \).

**Conclusion**: Both Reynolds number and coefficient of friction have the same dimensions.

### Step 2: Analyze Curie and Frequency of Light Wave
- **Curie (Ci)**: It is a unit of radioactivity, defined as the number of decays per second. Its dimension is \( T^{-1} \).
- **Frequency (ν)**: It is defined as the number of occurrences of a repeating event per unit time. Its dimension is also \( T^{-1} \).

**Conclusion**: Both Curie and frequency have the same dimensions.

### Step 3: Analyze Latent Heat and Gravitational Potential
- **Latent Heat (L)**: It is defined as the amount of heat required to change the phase of a substance per unit mass. Its dimension can be derived as follows:
- Heat has dimensions \( ML^2T^{-2} \).
- Mass has dimensions \( M \).
- Therefore, \( L = \frac{ML^2T^{-2}}{M} = L^2T^{-2} \).

- **Gravitational Potential (V)**: It is defined as the work done per unit mass in bringing a mass from infinity to a point in a gravitational field. Its dimension is calculated as:
- Work has dimensions \( ML^2T^{-2} \).
- Therefore, \( V = \frac{ML^2T^{-2}}{M} = L^2T^{-2} \).

**Conclusion**: Both latent heat and gravitational potential have the same dimensions.

### Step 4: Analyze Planck's Constant and Torque
- **Planck's Constant (h)**: It relates energy and frequency. From the equation \( E = hν \):
- Energy (E) has dimensions \( ML^2T^{-2} \).
- Frequency (ν) has dimensions \( T^{-1} \).
- Therefore, \( h = \frac{ML^2T^{-2}}{T^{-1}} = ML^2T^{-1} \).

- **Torque (τ)**: It is defined as the product of force and distance. The dimension is calculated as:
- Force has dimensions \( MLT^{-2} \).
- Distance has dimensions \( L \).
- Therefore, \( τ = MLT^{-2} \cdot L = ML^2T^{-2} \).

**Conclusion**: The dimensions of Planck's constant \( (ML^2T^{-1}) \) and torque \( (ML^2T^{-2}) \) are not the same.

### Final Conclusion
The pairs of physical quantities that have the same dimensions are:
1. Reynolds number and coefficient of friction.
2. Curie and frequency of light wave.
3. Latent heat and gravitational potential.

### Summary of Correct Options
The correct responses are options 1, 2, and 3.

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