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.
Choose the invariant quantities from the following

Options

A. mass
B. work
C. velocity
D. displacement

Answer

To solve the problem of identifying invariant quantities from the given options, we can follow these steps:

### Step 1: Understand the Concept of Invariant Quantities
Invariant quantities are those that have the same value regardless of the reference frame from which they are measured. In Newtonian mechanics, certain quantities are classified as invariant.

### Step 2: Identify the Invariant Quantities in Newtonian Mechanics
From the information provided, we know that:
- Invariant quantities include:
- Mass
- Time
- Force

### Step 3: Identify the Non-Invariant Quantities
The non-invariant quantities mentioned are:
- Displacement
- Velocity
- Work
- Kinetic Energy

### Step 4: Choose the Invariant Quantities
Based on the classifications:
- Mass is an invariant quantity.
- Time is also an invariant quantity.
- Force is an invariant quantity.

### Conclusion
From the given options, the invariant quantities are:
- Mass
- Time
- Force

### Final Answer
The invariant quantity from the options provided is **Mass**.

---