Which of the following sets cannot enter into the list of fundamental quatities in any system of units?

Options

A. length , mass and density
B. length , time and velocity
C. mass, time and velocity
D. length , time and mass

Explanation

To determine which set cannot enter into the list of fundamental quantities in any system of units, we need to analyze the options provided. Fundamental quantities are the basic physical quantities that are independent and cannot be derived from other quantities.

Let's evaluate each option step by step:

1. **Option A: Length, Mass, and Density**
- Length and mass are fundamental quantities.
- Density, however, is derived from mass and volume (Density = Mass/Volume).
- Since density can be expressed in terms of fundamental quantities (mass and length), this set can be included in the list of fundamental quantities.

2. **Option B: Length, Time, and Velocity**
- Length and time are fundamental quantities.
- Velocity is derived from length and time (Velocity = Length/Time).
- Since velocity can be expressed in terms of fundamental quantities, this set cannot be included in the list of fundamental quantities.

3. **Option C: Mass, Time, and Velocity**
- Mass and time are fundamental quantities.
- Velocity, again, is derived from length and time.
- Since velocity can be expressed in terms of fundamental quantities, this set cannot be included in the list of fundamental quantities.

4. **Option D: Length, Time, and Mass**
- All three quantities (length, time, and mass) are fundamental quantities and are independent of each other.
- Therefore, this set can be included in the list of fundamental quantities.

After analyzing all the options, we conclude that **Option B (Length, Time, and Velocity)** cannot enter into the list of fundamental quantities in any system of units because velocity is derived from length and time.

### Final Answer:
**Option B: Length, Time, and Velocity cannot enter into the list of fundamental quantities in any system of units.**