Which of the following depends on the choice of inertial reference frame ?

Options

A. Momentum
B. Change in momentum
C. Kinetic energy
D. Both (1) & (3)

Answer

To determine which of the following depends on the choice of inertial reference frame, we need to analyze the concepts of momentum, kinetic energy, and force.

### Step-by-Step Solution:

1. **Understanding Inertial Reference Frames**:
- An inertial reference frame is one in which Newton's laws of motion hold true. In such frames, objects either remain at rest or move at a constant velocity unless acted upon by a force.

2. **Analyzing Momentum**:
- Momentum (p) is defined as \( p = mv \), where \( m \) is mass and \( v \) is velocity.
- If we consider two different inertial frames, the velocity of an object can appear different in each frame. For example, if a vehicle is moving with velocity \( v \) and a person is moving with the same velocity, the relative velocity observed by the person will be zero.
- Therefore, momentum does depend on the choice of the inertial reference frame.

3. **Analyzing Kinetic Energy**:
- Kinetic energy (KE) is given by the formula \( KE = \frac{1}{2} mv^2 \).
- Similar to momentum, the kinetic energy will also vary depending on the velocity of the object as observed from different inertial frames. If two observers are moving at different velocities, they will calculate different kinetic energies for the same object.
- Thus, kinetic energy also depends on the choice of the inertial reference frame.

4. **Analyzing Force**:
- Force is defined as the rate of change of momentum, \( F = \frac{dp}{dt} \).
- While the force experienced by an object can be the same in different frames, the change in momentum (which is related to force) does not depend on the inertial frame when considering the same physical situation.
- Therefore, force does not depend on the choice of inertial reference frame.

5. **Conclusion**:
- From the analysis, we find that both momentum and kinetic energy depend on the choice of inertial reference frame, while force does not.
- Thus, the correct options are momentum and kinetic energy.

### Final Answer:
Momentum and kinetic energy depend on the choice of inertial reference frame.