If the resultant of all the external forces acting on a system of particles is zero. Then from an inertial frame, one can surely say that

Options

A. linear momentum of the system does not change time
B. kinetic energy of the system does not change in tire.
C. angular momentum of the system does not change time
D. potential energy of the system does not change in time

Explanation

To solve the problem, we need to analyze the implications of having a resultant external force of zero acting on a system of particles. Let's break it down step by step.

### Step-by-Step Solution:

1. **Understanding the Given Condition**:
- We are given that the resultant of all external forces acting on a system of particles is zero. This can be mathematically expressed as:
\[ \sum \vec{F}_{\text{external}} = 0 \]

2. **Applying Newton's Second Law**:
- According to Newton's second law, the net external force acting on a system is related to the acceleration of its center of mass (CM):
\[ \vec{F}_{\text{external}} = M \vec{a}_{\text{CM}} \]
- Where \( M \) is the total mass of the system and \( \vec{a}_{\text{CM}} \) is the acceleration of the center of mass.

3. **Implication of Zero External Force**:
- Since the resultant external force is zero, we can conclude:
\[ M \vec{a}_{\text{CM}} = 0 \]
- This implies that the acceleration of the center of mass is zero:
\[ \vec{a}_{\text{CM}} = 0 \]

4. **Constant Velocity of the Center of Mass**:
- If the acceleration of the center of mass is zero, then the velocity of the center of mass must be constant. Mathematically, this can be expressed as:
\[ \vec{v}_{\text{CM}} = \text{constant} \]

5. **Conservation of Linear Momentum**:
- The momentum of the system is defined as:
\[ \vec{P} = M \vec{v}_{\text{CM}} \]
- Since the velocity of the center of mass is constant, the linear momentum of the system must also be constant:
\[ \vec{P} = \text{constant} \]

6. **Conclusion**:
- From the above analysis, we can conclude that if the resultant of all external forces acting on a system of particles is zero, then the system's center of mass moves with a constant velocity, and the linear momentum of the system remains constant.

### Final Answer:
If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that the velocity of the center of mass is constant, and the linear momentum of the system is conserved.

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