Newton's laws of motion are applicable in all inertial reference frames. Some physical quantities, when measured by observers in different reference frames, have exactly the same value. Such physical quantities are called invariant. In Newtonian mechanics mass, time and force are invariant quantities . On the other hand, some physical quantities, when measured by observer in different reference frames, do not have the same value. Sigmae physical quantities are called not invariant . In Newtonian mechanics displacement, velocity and work ( which is the dot product of force and displacement) are not invariant. Also kinetic energy`(=1/2mv^(2))` is not invariant.
Physicists believe that all laws of physics are invariant in all inertial frames, i.e. the work-energy principle states that the change in the kinetic energy of a particle is equal to the work done on it by the force. Although, work and kinetic energy are not invariant in all reference frames, the work-energy principle remains invariant. Thus even though different observers measuring the motion of the same particle find different values of work and change in kinetic energy, they all find the work energy principle holds in their respective frames.
Which of the following quantities is invariant?

Options

A. Work
B. Kinetic energy
C. Vector
D. Displacement.

Answer

To determine which of the following quantities is invariant, we need to analyze the given information about invariant and non-invariant quantities in Newtonian mechanics.

### Step-by-Step Solution:

1. **Understanding Invariant Quantities**:
- Invariant quantities are those that have the same value in all inertial reference frames. According to the information provided, the invariant quantities in Newtonian mechanics are mass, time, and force.

2. **Identifying Non-Invariant Quantities**:
- Non-invariant quantities change their values when measured in different inertial reference frames. The non-invariant quantities mentioned are displacement, velocity, work, and kinetic energy.

3. **Analyzing Each Quantity**:
- **Mass**: This is an invariant quantity. It remains the same regardless of the reference frame.
- **Time**: This is also an invariant quantity. Time is measured the same way in all inertial frames.
- **Force**: This is an invariant quantity as well. It is calculated based on mass and acceleration, both of which are invariant.
- **Displacement**: This is a non-invariant quantity as it can change depending on the observer's frame of reference.
- **Velocity**: This is a non-invariant quantity since it is dependent on the frame of reference.
- **Work**: Work is defined as the dot product of force and displacement. Since displacement is non-invariant, work is also non-invariant.
- **Kinetic Energy**: Defined as \( KE = \frac{1}{2} mv^2 \). Since velocity is non-invariant, kinetic energy is also non-invariant.

4. **Conclusion**:
- The quantities that are invariant in Newtonian mechanics are mass, time, and force. Therefore, the answer to the question is that **mass, time, and force** are invariant quantities.

### Final Answer:
The invariant quantities are **mass, time, and force**.