Which of the following is/are correct?

Options

A. If centre of mass of three particles is at rest and it is known that two of them are moving along different lines, then the third particle must also be moving.
B. If centre of mass remains at rest, then net work done by the forces acting on the system must be zero.
C. If centre of mass remains at rest, then the net external force must be zero.
D. If speed of centre of mass is changing, then there must be some net work being done on the system from outside.

Explanation

To solve the question regarding the correctness of the given options related to the center of mass, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding Option A**:
- The statement claims that if the center of mass (COM) of three particles is at rest, then if two of them are moving along different lines, the third particle must also be moving.
- **Analysis**: If the center of mass is at rest, it implies that the total momentum of the system is zero. If two particles are moving in different directions, their momenta can cancel each other out, allowing the center of mass to remain stationary. Therefore, the third particle does not necessarily have to be moving.
- **Conclusion**: This statement is **incorrect**.

2. **Understanding Option B**:
- The statement claims that if the center of mass remains at rest, then the net work done by the forces acting on the system must be zero.
- **Analysis**: The net work done by external forces must be zero for the center of mass to remain at rest. However, internal forces can do work without affecting the center of mass. Therefore, this statement is misleading.
- **Conclusion**: This statement is **incorrect**.

3. **Understanding Option C**:
- The statement claims that if the center of mass remains at rest, then the net external force must be zero.
- **Analysis**: This is a fundamental principle in physics. If the center of mass of a system is not accelerating, it means that the net external force acting on it is indeed zero.
- **Conclusion**: This statement is **correct**.

4. **Understanding Option D**:
- The statement claims that if the speed of the center of mass is changing, then there must be some net work being done on the system from the outside.
- **Analysis**: If the speed of the center of mass is changing, it indicates that there is a net external force acting on the system, which results in net work being done. Thus, this statement is true.
- **Conclusion**: This statement is **correct**.

### Final Answers:
Based on the analysis:
- **Correct Options**: C and D.