A particle is observed from two frames `S_1 and S_2.` Lthe frame `S_2` moves with respect to`S_1` with an acceleration a. Let `F_1 and F_2` be the pseudo forces on the particle when seen from `S_1 and S_2` respectively. Which of the following are not possible/

Options

A. `F_1=0,F_2!=0`
B. `F_1!=0, F_2=0`
C. `F_1!=0, F_2!=0`
D. `F_1=0, F_2=0`

Answer

To solve the problem, we need to analyze the pseudo forces acting on a particle observed from two different frames of reference, \( S_1 \) and \( S_2 \). The frame \( S_2 \) is moving with respect to \( S_1 \) with an acceleration \( a \). We will evaluate the four scenarios presented in the question regarding the pseudo forces \( F_1 \) and \( F_2 \).

### Step-by-Step Solution:

1. **Understanding Pseudo Forces**:
- A pseudo force is an apparent force that acts on an object when viewed from a non-inertial frame of reference.
- If a frame is accelerating, an observer in that frame will perceive a pseudo force acting on objects within that frame.

2. **Analyzing the First Condition**: \( F_1 = 0 \) and \( F_2 \neq 0 \)
- If \( F_1 = 0 \), it implies that frame \( S_1 \) is either at rest or moving with a constant velocity (inertial frame).
- Since \( S_2 \) is accelerating with respect to \( S_1 \), \( F_2 \) must be non-zero.
- **Conclusion**: This condition is possible.

3. **Analyzing the Second Condition**: \( F_1 \neq 0 \) and \( F_2 = 0 \)
- If \( F_1 \neq 0 \), it means that frame \( S_1 \) is accelerating.
- If \( F_2 = 0 \), it means that frame \( S_2 \) is inertial (not accelerating).
- However, since \( S_2 \) is defined to be accelerating with respect to \( S_1 \), this condition cannot hold.
- **Conclusion**: This condition is not possible.

4. **Analyzing the Third Condition**: \( F_1 \neq 0 \) and \( F_2 \neq 0 \)
- If both \( F_1 \) and \( F_2 \) are non-zero, it indicates that both frames \( S_1 \) and \( S_2 \) are accelerating.
- This is a valid scenario as both frames can have their own accelerations.
- **Conclusion**: This condition is possible.

5. **Analyzing the Fourth Condition**: \( F_1 = 0 \) and \( F_2 = 0 \)
- If both pseudo forces are zero, it means both frames are inertial frames (not accelerating).
- However, since \( S_2 \) is defined to be accelerating with respect to \( S_1 \), this condition cannot hold.
- **Conclusion**: This condition is not possible.

### Final Answer:
The conditions that are **not possible** are:
- \( F_1 \neq 0 \) and \( F_2 = 0 \)
- \( F_1 = 0 \) and \( F_2 = 0 \)