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 and kinetic energy, as well as their dependence on the reference frame.

### Step-by-Step Solution:

1. **Understanding Momentum**:
- Momentum (p) is defined as the product of mass (m) and velocity (v):
\[ p = mv \]
- The velocity of an object can change depending on the observer's frame of reference. For instance, if an object is moving in a car, an observer on the ground will see a certain velocity, while an observer in the car will see the object as stationary (relative velocity = 0).

2. **Momentum in Different Reference Frames**:
- If the observer is at rest (inertial frame 1) and sees the object moving with velocity \( v \), the momentum will be \( mv \).
- If another observer is moving with the same velocity as the object (inertial frame 2), they will see the momentum as:
\[ p' = m(0) = 0 \]
- This shows that momentum depends on the choice of the inertial reference frame.

3. **Understanding Kinetic Energy**:
- Kinetic energy (KE) is given by the formula:
\[ KE = \frac{1}{2} mv^2 \]
- Similar to momentum, the kinetic energy of an object will also vary based on the observer's frame of reference.

4. **Kinetic Energy in Different Reference Frames**:
- For an observer at rest (inertial frame 1), if the object has velocity \( v \), the kinetic energy will be:
\[ KE = \frac{1}{2} mv^2 \]
- If another observer is moving with velocity \( v_1 \) (inertial frame 2), the relative velocity of the object will be \( v - v_1 \), leading to a different kinetic energy:
\[ KE' = \frac{1}{2} m(v - v_1)^2 \]
- This demonstrates that kinetic energy also depends on the choice of the inertial reference frame.

5. **Conclusion**:
- Both momentum and kinetic energy depend on the choice of the inertial reference frame. However, the question asks for which of the following depends on the choice of inertial reference frame, leading us to conclude that both momentum and kinetic energy are dependent on the reference frame.

### Final Answer:
The correct option is that both momentum and kinetic energy depend on the choice of inertial reference frame.