Newton's law are valid in

Options

A. any reference frame
B. a frame moving with constant velocity w.r.t. an inertial fame.
C. all reference frames which are at rest w.r.t. an inertial frame.
D. the reference frame attached to the earth.

Answer

To determine the validity of Newton's laws of motion, we need to identify the type of reference frames in which these laws hold true. Here's a step-by-step solution:

### Step 1: Understand Newton's Laws of Motion
Newton's laws of motion consist of three fundamental principles that describe the relationship between the motion of an object and the forces acting on it. These laws are:
1. **First Law**: An object at rest stays at rest, and an object in motion continues in motion with the same speed and in the same direction unless acted upon by a net external force.
2. **Second Law**: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (F = ma).
3. **Third Law**: For every action, there is an equal and opposite reaction.

### Step 2: Identify Inertial and Non-Inertial Frames
- **Inertial Frame**: A reference frame in which an object either remains at rest or moves at a constant velocity unless acted upon by a net external force. In this frame, the acceleration is zero.
- **Non-Inertial Frame**: A reference frame that is accelerating. In this frame, fictitious forces may appear, and Newton's laws do not apply without modification.

### Step 3: Determine Validity of Newton's Laws
Newton's laws are valid in inertial frames. This means:
- The frame must either be at rest or moving with a constant velocity (which implies zero acceleration).
- If the frame is accelerating (like a lift moving upward with acceleration), it is a non-inertial frame, and Newton's laws cannot be applied directly.

### Step 4: Analyze the Given Options
- **Option A**: Any reference frame - Incorrect, as Newton's laws are not valid in non-inertial frames.
- **Option B**: Frame moving with constant velocity with respect to an inertial frame - Correct, as this is an inertial frame.
- **Option C**: Reference frame which is at rest with respect to an inertial frame - Correct, as this is also an inertial frame.
- **Option D**: Reference frame which is attached to the Earth - Incorrect, since the Earth can be considered a non-inertial frame due to its rotation and other factors.

### Conclusion
The correct options where Newton's laws are valid are **B** and **C**.

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