Consider the following two statements:
A The linear momentum of a particle is independent of the frame of reference.
B. The kinetic energy of a particle is independent of the frame of reference

Options

A. both A and B are true
B. A is true but B is false
C. Ais false but B is true
D. both A and B are false

Answer

To analyze the two statements regarding linear momentum and kinetic energy in relation to the frame of reference, we can break down the solution step by step.

### Step 1: Understanding Linear Momentum
Linear momentum (p) of a particle is defined as:
\[ p = m \cdot v \]
where \( m \) is the mass and \( v \) is the velocity of the particle.

### Step 2: Frame of Reference for Linear Momentum
- In an **inertial frame** (a non-accelerating frame), the linear momentum of a particle is consistent and does not depend on the observer's motion.
- In a **non-inertial frame** (an accelerating frame), pseudo forces come into play. The velocity of the particle as perceived in this frame can change due to these pseudo forces, affecting the linear momentum.

### Conclusion for Statement A
Thus, **Statement A** (The linear momentum of a particle is independent of the frame of reference) is **false** because it is dependent on the frame of reference, especially in non-inertial frames.

### Step 3: Understanding Kinetic Energy
Kinetic energy (KE) is defined as:
\[ KE = \frac{1}{2} m v^2 \]

### Step 4: Frame of Reference for Kinetic Energy
- Similar to linear momentum, in an **inertial frame**, the kinetic energy is straightforwardly calculated based on the velocity of the particle.
- In a **non-inertial frame**, the velocity can change due to the effects of pseudo forces, which means the kinetic energy can also change as it depends on the square of the velocity.

### Conclusion for Statement B
Thus, **Statement B** (The kinetic energy of a particle is independent of the frame of reference) is also **false** because it is dependent on the frame of reference due to the effects of pseudo forces.

### Final Conclusion
Both statements A and B are false.

### Summary of the Solution
- Statement A: False (linear momentum is dependent on the frame of reference).
- Statement B: False (kinetic energy is dependent on the frame of reference).
- Therefore, the correct option is that both A and B are false.

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