For a two `-` body sstem in absence of external forces, the kinetic energy as measured from ground frame is `K_(0)` and from centre of mass frame is `K_(cm)`. Pick up the wrong statement.

Options

A. The kinetic energy as measured from center of mass frame is least
B. Only the portion of energy `K_(cm)` can be transferred from one form to another due to internal changes in the system.
C. The system always retains at least `K_(o)-K_(cm)` amount of kinetic energy as measured from ground frame irrespective of any kind of internal changes in the system.
D. The system always retains at least `K_(cm)` amount of kinetic energy as measured from ground frame irrespective of any kind of internal changes in the system.

Explanation

To solve the problem, we need to analyze the relationship between the kinetic energy measured from the ground frame (K₀) and the kinetic energy measured from the center of mass frame (K_cm) for a two-body system in the absence of external forces. We will also identify the wrong statement among the given options.

### Step-by-Step Solution:

1. **Understanding Kinetic Energy in Different Frames**:
- The kinetic energy of a system can be measured from different reference frames. In this case, we have two frames: the ground frame and the center of mass frame.

2. **Kinetic Energy from the Ground Frame (K₀)**:
- The total kinetic energy measured from the ground frame (K₀) can be expressed as:
\[ K₀ = K_{cm} + \frac{1}{2} M v_{cm}^2 \]
where:
- \( K_{cm} \) is the kinetic energy measured from the center of mass frame.
- \( M \) is the total mass of the system.
- \( v_{cm} \) is the velocity of the center of mass with respect to the ground.

3. **Kinetic Energy from the Center of Mass Frame (K_cm)**:
- The kinetic energy in the center of mass frame (K_cm) is the kinetic energy of the system as observed from the center of mass. It does not include the translational kinetic energy due to the motion of the center of mass itself.

4. **Analyzing the Statements**:
- We need to evaluate the statements provided in the question to identify the incorrect one. The relationship derived above shows that K₀ is always greater than or equal to K_cm, as it includes the additional term \(\frac{1}{2} M v_{cm}^2\).

5. **Conclusion**:
- Since K₀ includes the kinetic energy due to the motion of the center of mass, it cannot be less than K_cm. Therefore, any statement suggesting that K₀ can be less than K_cm or that K_cm can be greater than K₀ would be incorrect.

### Final Answer:
The wrong statement is one that suggests \( K₀ < K_{cm} \) or any similar relationship that contradicts the derived equation.