Is net work done by all the external force of a system is independent of choice of reference frame.

Answer

To determine whether the net work done by all external forces of a system is independent of the choice of reference frame, we can analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding Work Done**:
Work done (W) by a force is defined as the product of the force (F) and the displacement (d) in the direction of the force. Mathematically, it can be expressed as:
\[ W = F \cdot d \]

2. **Choosing a Reference Frame**:
Let's consider a block of mass \( m \) subjected to an external force \( F \) acting to the right. The block accelerates with an acceleration \( a \).

3. **Inertial Reference Frame**:
In an inertial reference frame (a stationary frame), the work done by the external force can be calculated using the displacement of the block as it moves under the influence of the force \( F \).

4. **Non-Inertial Reference Frame**:
Now, consider a non-inertial reference frame that is accelerating to the right with the same acceleration \( a \) as the block. In this frame, the block appears to be at rest because both the block and the frame are moving together.

5. **Calculating Work Done in Different Frames**:
- In the inertial frame, the work done by the force \( F \) is positive because the force causes displacement in the direction of the force.
- In the non-inertial frame, since the block does not move relative to this frame, the displacement \( d \) is zero. Therefore, the work done by the external force in this frame is:
\[ W = F \cdot 0 = 0 \]

6. **Conclusion**:
Since the work done by the external force is different in the two reference frames (non-zero in the inertial frame and zero in the non-inertial frame), we conclude that the net work done by all external forces of a system is **dependent** on the choice of reference frame.

### Final Answer:
No, the net work done by all external forces of a system is dependent on the choice of reference frame.

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