Which of the following can be a set of fundamental quantities.

Options

A. length, velocity, time
B. momentum, mass , velocity
C. force, mass , velocity
D. momentum, time , frequency

Answer

To determine which set of quantities can be considered fundamental, we need to ensure that none of the quantities in the set can be expressed in terms of the others. Let's analyze each option step by step:

### Option A: Length, Velocity, Time
- **Length (L)**
- **Velocity (V)**: Velocity is defined as \( V = \frac{L}{T} \), where \( L \) is length and \( T \) is time.
- **Time (T)**

Since velocity can be expressed in terms of length and time, this set cannot be fundamental.

### Option B: Momentum, Mass, Velocity
- **Momentum (P)**: Momentum is defined as \( P = MV \), where \( M \) is mass and \( V \) is velocity.
- **Mass (M)**
- **Velocity (V)**

Since momentum can be expressed in terms of mass and velocity, this set cannot be fundamental.

### Option C: Force, Mass, Velocity
- **Force (F)**: Force is defined as \( F = MA \), where \( M \) is mass and \( A \) is acceleration.
- **Mass (M)**
- **Velocity (V)**

Force cannot be directly expressed in terms of mass and velocity alone; it requires acceleration. Therefore, this set could potentially be fundamental.

### Option D: Momentum, Time, Frequency
- **Momentum (P)**: Momentum is defined as \( P = MV \), where \( M \) is mass and \( V \) is velocity.
- **Time (T)**
- **Frequency (F)**: Frequency is defined as \( F = \frac{1}{T} \), where \( T \) is time.

Since frequency can be expressed in terms of time, this set cannot be fundamental.

### Conclusion
The only set where none of the quantities can be expressed in terms of the others directly is Option C: Force, Mass, Velocity.

Therefore, the correct answer is:
**C: Force, Mass, Velocity**

### Step-by-Step Solution:
1. **Identify the quantities in each set**:
- Option A: Length, Velocity, Time
- Option B: Momentum, Mass, Velocity
- Option C: Force, Mass, Velocity
- Option D: Momentum, Time, Frequency

2. **Check if any quantity can be expressed in terms of the others**:
- **Option A**: Velocity \( V = \frac{L}{T} \) (Not fundamental)
- **Option B**: Momentum \( P = MV \) (Not fundamental)
- **Option C**: Force \( F = MA \) (Potentially fundamental)
- **Option D**: Frequency \( F = \frac{1}{T} \) (Not fundamental)

3. **Determine the set where none of the quantities are dependent on each other**:
- **Option C**: Force, Mass, Velocity (None of these can be expressed directly in terms of the others)

4. **Conclude the correct set of fundamental quantities**:
- **Option C: Force, Mass, Velocity**