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

Options

A. volumetric strain and coefficient of friction
B. disintegration constant of a radioactive substance and frequency of light wave
C. heat capacity and gravitational potential
D. Stefan's constant and Wien's constant

Answer

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

### Step-by-Step Solution:

1. **Understanding the Physical Quantities**:
- We need to identify the dimensions of the given physical quantities in the options.

2. **Analyzing the First Option**:
- **Volumetric Strain**:
- Volumetric strain is defined as the change in volume divided by the original volume.
- It is a dimensionless quantity because it is a ratio of two volumes (both have the same dimensions).
- Dimensions: [L^3]/[L^3] = 1 (dimensionless).
- **Coefficient of Friction**:
- The coefficient of friction is defined as the ratio of the force of friction to the normal force.
- Both forces have the same dimensions (mass × acceleration), hence it is also dimensionless.
- Dimensions: [M L T^-2]/[M L T^-2] = 1 (dimensionless).
- **Conclusion**: Both volumetric strain and coefficient of friction are dimensionless, hence they have the same dimensions.

3. **Analyzing the Second Option**:
- **Disintegration Constant (Decay Constant)**:
- The decay constant (λ) is defined as the number of decays per unit time.
- Dimensions: [1/T] = T^-1.
- **Frequency**:
- Frequency (f) is defined as the number of cycles per unit time.
- Dimensions: [1/T] = T^-1.
- **Conclusion**: Both the disintegration constant and frequency have the same dimensions (T^-1).

4. **Final Conclusion**:
- The pairs of physical quantities that have the same dimensions are:
- **Volumetric Strain and Coefficient of Friction** (both dimensionless).
- **Disintegration Constant and Frequency** (both have dimensions T^-1).

### Answer:
The pairs of physical quantities that have the same dimensions are:
1. Volumetric Strain and Coefficient of Friction (dimensionless).
2. Disintegration Constant and Frequency (T^-1).