Which of the following set(s) of quantity (ies) can replace mass, length and time in the set of fundamental quantities.

Options

A. Density area and frequency
B. Force, power and velocity
C. Speed, acceleration and volume
D. Forcem, density and velocity

Answer

To determine which set of quantities can replace mass, length, and time in the set of fundamental quantities, we will analyze each option provided in the question.

### Step-by-Step Solution:

1. **Understanding Fundamental Quantities**:
- Fundamental quantities are the basic physical quantities that cannot be defined in terms of other quantities. The three fundamental quantities we are considering are mass (M), length (L), and time (T).

2. **Analyzing Option 1: Density, Area, and Frequency**:
- **Density (ρ)**: Density is defined as mass per unit volume (ρ = M/V). While it involves mass, it is not a fundamental quantity on its own because it is derived from mass and volume.
- **Area (A)**: Area is defined as length squared (A = L²). It is derived from length and therefore cannot replace length as a fundamental quantity.
- **Frequency (f)**: Frequency is defined as the reciprocal of time (f = 1/T). It is related to time but cannot replace time as a fundamental quantity.
- **Conclusion**: This set does not consist of fundamental quantities.

3. **Analyzing Option 2: Force, Power, and Velocity**:
- **Force (F)**: Force is defined as mass times acceleration (F = M*a). It is derived from mass and cannot replace it.
- **Power (P)**: Power is defined as work done per unit time (P = W/T). It is derived from work and time and cannot replace either.
- **Velocity (v)**: Velocity is defined as displacement per unit time (v = d/T). It is derived from length and time and cannot replace either.
- **Conclusion**: This set does not consist of fundamental quantities.

4. **Analyzing Option 3: Speed, Acceleration, and Volume**:
- **Speed (v)**: Speed is defined as distance traveled per unit time (v = d/T). It is derived from length and time and cannot replace either.
- **Acceleration (a)**: Acceleration is defined as the change in velocity per unit time (a = Δv/T). It is derived from length and time and cannot replace either.
- **Volume (V)**: Volume is defined as length cubed (V = L³). It is derived from length and cannot replace it.
- **Conclusion**: This set does not consist of fundamental quantities.

5. **Analyzing Option 4: Force, Density, and Velocity**:
- **Force (F)**: As mentioned earlier, force is derived from mass and cannot replace it.
- **Density (ρ)**: Density is derived from mass and volume and cannot replace mass.
- **Velocity (v)**: Velocity is derived from length and time and cannot replace either.
- **Conclusion**: This set does not consist of fundamental quantities.

### Final Conclusion:
After analyzing all the options, none of the sets provided can completely replace mass, length, and time as fundamental quantities.