Two frame `S_(1)` and `S_(2)` are non-inertial. Then frame `S_(2)` when observed from `S_(1)` is inertial.
A frame in motion is not necessarily a non-inertial frame

Options

A. The relative acceleration of the frame may either be zero or `4ms^(-2)`
B. Their relative acceleration may have any value between `0 and 4 ms^(-2)`.
C. Both the frames may be stationary with respect to earth.
D. The frames may be moving with same acceleration in same direction.

Explanation

To solve the problem, we need to analyze the concepts of inertial and non-inertial frames of reference.

### Step-by-Step Solution:

1. **Define Inertial and Non-Inertial Frames**:
- An **inertial frame** is one in which Newton's first law holds true, meaning that an object at rest stays at rest, and an object in motion continues in motion with a constant velocity unless acted upon by a net external force. This frame has zero acceleration.
- A **non-inertial frame** is one that is accelerating with respect to an inertial frame. In such frames, fictitious forces (like centrifugal force or Coriolis force) appear to act on objects.

2. **Given Information**:
- We have two frames, \( S_1 \) and \( S_2 \), both of which are non-inertial. This means both frames are accelerating.

3. **Observation from Frame \( S_1 \)**:
- When we observe frame \( S_2 \) from frame \( S_1 \), we need to analyze the relative acceleration between the two frames.

4. **Acceleration Relationship**:
- Let \( a_{S_1} \) be the acceleration of frame \( S_1 \) and \( a_{S_2} \) be the acceleration of frame \( S_2 \).
- Since both frames are non-inertial, they have non-zero accelerations. However, when we say that frame \( S_2 \) is observed from \( S_1 \) as inertial, we imply that the relative acceleration between the two frames is zero. This can be expressed as:
\[ a_{S_1} - a_{S_2} = 0 \]
- This simplifies to:
\[ a_{S_1} = a_{S_2} \]
- This means that both frames are accelerating at the same rate.

5. **Conclusion**:
- Therefore, even though both frames \( S_1 \) and \( S_2 \) are non-inertial, they can be moving with the same acceleration in the same direction. Thus, when viewed from \( S_1 \), \( S_2 \) can appear to be inertial.

### Final Answer:
The correct interpretation is that both non-inertial frames \( S_1 \) and \( S_2 \) can have equal accelerations, making \( S_2 \) appear inertial when observed from \( S_1 \).

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