Choose the correct statement about the center mass of a body,

Options

A. Center of mass always lies outside the body
B. Center of mass always lies inside the body
C. Position of center of mass relative to the body depends on the choice of origin
D. Center of mass may either lie inside or outside the body

Answer

To solve the question about the center of mass of a body, we need to analyze the statements provided and determine which one is correct.

### Step-by-Step Solution:

1. **Understanding Center of Mass**: The center of mass (COM) of a body is a point that represents the average position of all the mass in the body. It is the point where the total mass of the system can be considered to be concentrated for the purpose of analyzing translational motion.

2. **Position of the Center of Mass**: The center of mass can be located either inside or outside the physical boundaries of the body. For example, in a uniform rod, the center of mass is at its midpoint, which is inside the rod. In contrast, for a ring or a hollow sphere, the center of mass is at the center, which is inside the body, but for a system of particles, it could also be outside depending on their arrangement.

3. **Evaluating the Statements**:
- **Statement 1**: "Center of mass always lies outside the body." - This is incorrect because the center of mass can be inside the body as well.
- **Statement 2**: "Position of the center of mass relative to the body depends on the choice of origin." - This statement is misleading. While the calculation of the center of mass can depend on the coordinate system used, the physical location of the center of mass does not change with the choice of origin.
- **Statement 3**: "Center of mass may either lie inside or outside the body." - This statement is correct as explained earlier.
- **Statement 4**: "Center of mass is a point in which the moment of mass is zero." - This statement is incorrect; the center of mass is not defined by the moment of mass being zero.

4. **Conclusion**: The correct statement about the center of mass of a body is that it may either lie inside or outside the body.

### Final Answer:
The correct statement is: "Center of mass may either lie inside or outside the body."