(A) : A particle is found to be at rest when seen from a frame S,and moving with a constant velocity when seen from another frame `S_2`. We can say both the frames are inertial
( R) : All frames moving uniformly with respect to an inertial frame are themselves inertial

Options

A. Both (A) and (R) are true and (R) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not the
C. (A) is true but ( R) is false
D. Both (A) and (R ) are false

Answer

To solve the question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step 1: Understand the Assertion (A)
The assertion states that a particle is at rest in frame S and is moving with a constant velocity in frame S2. We need to determine if both frames can be considered inertial frames.

- **Inertial Frame Definition**: An inertial frame is one in which Newton's first law holds true, meaning that an object either remains at rest or moves at a constant velocity unless acted upon by a net external force.

### Step 2: Analyze Frame S
In frame S, the particle is at rest. This means there is no net force acting on the particle, and thus frame S can be classified as an inertial frame.

### Step 3: Analyze Frame S2
In frame S2, the particle is moving with a constant velocity. This also indicates that there is no net force acting on the particle in this frame. Therefore, frame S2 can also be classified as an inertial frame.

### Step 4: Conclusion for Assertion (A)
Since both frames S and S2 do not experience any acceleration and adhere to the laws of motion, we can conclude that both frames are indeed inertial frames.

### Step 5: Understand the Reason (R)
The reason states that all frames moving uniformly with respect to an inertial frame are themselves inertial.

- **Explanation of Reason (R)**: If we have an inertial frame (let's say frame S), and another frame (let's say frame S2) is moving with a constant velocity relative to frame S, then frame S2 will also not experience any acceleration. Thus, it will also be an inertial frame.

### Step 6: Conclusion for Reason (R)
The reason is true because it correctly describes the relationship between inertial frames. Any frame moving uniformly with respect to an inertial frame is also inertial.

### Final Conclusion
Both the assertion (A) and the reason (R) are true. However, the reason does not serve as a direct explanation for the assertion. Therefore, the correct answer is that both A and R are true, but R is not the correct explanation of A.

### Summary of the Solution
- Assertion (A) is true: Both frames S and S2 are inertial.
- Reason (R) is true: All frames moving uniformly with respect to an inertial frame are themselves inertial.
- The correct option is: Both A and R are true, but R is not the correct explanation of A.