Net external force acting on a system of particle is not equal to zero. If velocity and acceleration of the centre of mass of the system of particles at some instant of time are found to be v and a respectively select possible option (s).

Options

A. `v=0 and a=0`
B. `v ne 0and a ne0`
C. `v ne 0 and a=0`
D. `v=0 and a ne 0`

Explanation

To solve the problem, we need to analyze the situation based on the information provided about the net external force, velocity, and acceleration of the center of mass of a system of particles.

### Step-by-Step Solution:

1. **Understanding the System**:
- We have a system of particles where the net external force acting on it is not equal to zero. This means that there is a resultant force causing the system to accelerate.

2. **Applying Newton's Second Law**:
- According to Newton's second law of motion, the net external force (\(F_{\text{net}}\)) acting on a system is equal to the mass (\(m\)) of the system multiplied by the acceleration (\(a\)) of the center of mass:
\[ F_{\text{net}} = m \cdot a \]
- Since \(F_{\text{net}} \neq 0\), it implies that the acceleration of the center of mass (\(a\)) must also be non-zero:
\[ a \neq 0 \]

3. **Analyzing the Velocity of the Center of Mass**:
- The velocity (\(v\)) of the center of mass can be either zero or non-zero, depending on the state of motion of the system.
- For example, if a ball is thrown up, at its highest point, the velocity is zero, but there is still a gravitational force acting on it, hence \(F_{\text{net}} \neq 0\).

4. **Evaluating the Options**:
- **Option A**: Acceleration of the center of mass is zero. (This is incorrect because we established that \(a \neq 0\)).
- **Option B**: Velocity of the center of mass is not equal to zero. (This can be correct, but it is not necessarily true since \(v\) can be zero at a specific moment).
- **Option C**: Acceleration of the center of mass is zero. (This is incorrect for the same reason as Option A).
- **Option D**: Velocity of the center of mass can be zero. (This is correct, as explained with the example of the ball).

5. **Conclusion**:
- The correct options are:
- Option B (Velocity of the center of mass is not equal to zero) can be true in general but not necessarily at all times.
- Option D (Velocity of the center of mass can be zero) is definitely true at specific instances.

### Final Answer:
- The possible correct options are **B and D**.