Consider the following two statements .
A : Kinetic energy depends on frame of reference .
B : Linear momentum does not depend on frame of reference .

Options

A. Both A and B are false .
B. Both A and B are true .
C. A is true and B is false .
D. B is true and A is false .

Explanation

To analyze the statements regarding kinetic energy and linear momentum, we will evaluate each statement step by step.

### Step 1: Understanding Kinetic Energy
Kinetic energy (KE) is given by the formula:
\[ KE = \frac{1}{2} mv^2 \]
where:
- \( m \) is the mass of the object,
- \( v \) is the velocity of the object.

### Step 2: Dependency of Kinetic Energy on Frame of Reference
1. The mass \( m \) of an object is invariant; it does not change with the frame of reference.
2. However, the velocity \( v \) of the object does depend on the observer's frame of reference. For example, if an observer is moving with a certain velocity, they will measure different velocities for the same object compared to an observer at rest.
3. Since kinetic energy depends on the square of the velocity, and velocity changes with the frame of reference, it follows that kinetic energy also changes with the frame of reference.

**Conclusion for Statement A**: Kinetic energy depends on the frame of reference. Thus, Statement A is **True**.

### Step 3: Understanding Linear Momentum
Linear momentum (p) is given by the formula:
\[ p = mv \]
where:
- \( m \) is the mass of the object,
- \( v \) is the velocity of the object.

### Step 4: Dependency of Linear Momentum on Frame of Reference
1. Similar to kinetic energy, the mass \( m \) remains constant across different frames of reference.
2. The velocity \( v \) of the object, however, varies depending on the observer's frame of reference.
3. Therefore, since momentum is the product of mass and velocity, and velocity changes with the frame of reference, linear momentum also depends on the frame of reference.

**Conclusion for Statement B**: Linear momentum does depend on the frame of reference. Thus, Statement B is **False**.

### Final Conclusion
- Statement A: True (Kinetic energy depends on frame of reference)
- Statement B: False (Linear momentum does depend on frame of reference)

### Summary of Answers
- A is True
- B is False