The pair (s) of physical quantities that have same dimension, is (are) :

Options

A. Reyonld number and coefficient of fricttion
B. Latent heat and gravitational potential
C. Currie and frequency of a light
D. Planck's constant and torque

Answer

To determine the pairs of physical quantities that have the same dimension, we will analyze each pair given in the problem step by step.

### Step 1: Analyze Reynolds Number and Coefficient of Friction
- **Reynolds Number**: It is a dimensionless quantity, which means it has no dimensions.
- **Coefficient of Friction**: It is also dimensionless, calculated as the ratio of frictional force to normal force, both of which have the dimension of force (MLT^-2). Thus, the coefficient of friction is also dimensionless.

**Conclusion**: Both Reynolds number and coefficient of friction are dimensionless.

### Step 2: Analyze Latent Heat and Gravitational Potential
- **Latent Heat (L)**: It is defined as the amount of heat (Q) required to change the state of a unit mass (m) without changing its temperature. The formula is Q = m * L.
- Dimensions of Q (energy) = ML²T⁻²
- Dimensions of m (mass) = M
- Therefore, dimensions of latent heat (L) = Q/m = (ML²T⁻²)/M = L²T⁻².

- **Gravitational Potential (U)**: It is defined as the potential energy (U) per unit mass (m).
- Dimensions of U (potential energy) = ML²T⁻²
- Therefore, dimensions of gravitational potential = U/m = (ML²T⁻²)/M = L²T⁻².

**Conclusion**: Both latent heat and gravitational potential have the same dimensions (L²T⁻²).

### Step 3: Analyze Curie and Frequency of Light
- **Curie (Ci)**: It is a unit of radioactivity and is defined as the number of disintegrations per second.
- Dimensions of Curie = 1/time = T⁻¹.

- **Frequency of Light**: It is defined as the reciprocal of the time period (T).
- Dimensions of frequency = 1/time = T⁻¹.

**Conclusion**: Both Curie and frequency of light have the same dimensions (T⁻¹).

### Step 4: Analyze Planck's Constant and Torque
- **Planck's Constant (h)**: It relates energy (E) to frequency (ν). The formula is E = hν.
- Dimensions of E (energy) = ML²T⁻².
- Dimensions of frequency (ν) = T⁻¹.
- Therefore, dimensions of Planck's constant = E/ν = (ML²T⁻²)/(T⁻¹) = ML²T⁻¹.

- **Torque (τ)**: It is defined as the product of force (F) and the distance (R) from the pivot point.
- Dimensions of force (F) = MLT⁻².
- Dimensions of distance (R) = L.
- Therefore, dimensions of torque = R * F = L * (MLT⁻²) = ML²T⁻².

**Conclusion**: Planck's constant (ML²T⁻¹) and torque (ML²T⁻²) have different dimensions.

### Final Conclusion
The pairs of physical quantities that have the same dimensions are:
1. Reynolds Number and Coefficient of Friction (Dimensionless)
2. Latent Heat and Gravitational Potential (L²T⁻²)
3. Curie and Frequency of Light (T⁻¹)

### Answer
The correct options are 1, 2, and 3.

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