Select the correct option.

Options

A. if centre of mass remains at rest then net work done by the forces acting on the system must be zero
B. is centre of mass remains at rest ,then the net external force must be zero
C. its centre of mass moving with constant velocity then the net external force must be zero
D. Both(2) and (3)

Answer

To solve the question, we need to analyze the options provided regarding the center of mass and the forces acting on a system. Let's break it down step by step.

### Step 1: Understand the Concept of Center of Mass
The center of mass (COM) of a system is a point that represents the average position of all the mass in the system. If no external forces act on the system, the center of mass will either remain at rest or move with a constant velocity.

**Hint:** Remember that the motion of the center of mass is determined by the net external forces acting on the system.

### Step 2: Analyze Option 1
The first option states that "the work done by the force acting on the system must be zero." According to the work-energy theorem, the work done by all forces acting on a system is equal to the change in kinetic energy of that system. If the center of mass is moving, work done cannot be zero unless there is no change in kinetic energy, which is not necessarily true.

**Hint:** Recall the work-energy theorem: Work done = Change in kinetic energy.

### Step 3: Analyze Option 2
The second option states that "if the center of mass remains at rest, then the net external force must be zero." This is true. If the net external force acting on a system is zero, the center of mass will not accelerate, meaning it can either remain at rest or move with constant velocity.

**Hint:** Consider Newton's first law: An object at rest stays at rest unless acted upon by a net external force.

### Step 4: Analyze Option 3
The third option states that "if the center of mass is moving with constant velocity, then the net external force must also be zero." This is also true. If the center of mass is moving with constant velocity, it implies that there is no net external force acting on the system (again, according to Newton's first law).

**Hint:** Think about the implications of constant velocity on acceleration and net force.

### Step 5: Conclusion
Based on the analysis:
- Option 1 is false.
- Option 2 is true.
- Option 3 is true.

Thus, the correct answer is option 4, which states that both options 2 and 3 are correct.

**Final Answer:** Option 4 (Both 2 and 3 are correct).