Which one of the following statements is true?

Options

A. the center of mass of an object must lie within the object
B. all the mass of an object is actually concentrated at its center of mass
C. the center of mass of an object cannot move if there is zero net force on the object
D. None of the above

Explanation

To determine which statement is true regarding the center of mass (COM) of an object, let's analyze each option step by step.

### Step 1: Analyze the first statement
**Statement:** The center of mass of an object must lie within the object.

**Analysis:** This statement is false. The center of mass does not have to be located within the physical boundaries of the object. For example, consider a circular ring. The center of mass of a ring is at its center, which is a point in space that does not contain any mass. Therefore, this statement is incorrect.

### Step 2: Analyze the second statement
**Statement:** All the mass of an object is actually concentrated at its center of mass.

**Analysis:** This statement is misleading. While it is a common assumption for translational motion that the entire mass can be considered to be concentrated at the center of mass for the purpose of analysis, it does not hold true for rotational motion. In rotational dynamics, the distribution of mass around the center of mass affects the moment of inertia. Thus, this statement is also incorrect.

### Step 3: Analyze the third statement
**Statement:** The center of mass of an object cannot move if there is zero net force on the object.

**Analysis:** This statement is incorrect. If there is zero net force acting on an object, it means that the center of mass can either remain at rest or move with a constant velocity. According to Newton's first law of motion, an object in motion will remain in motion unless acted upon by a net external force. Therefore, this statement is false.

### Step 4: Analyze the fourth statement
**Statement:** None of these above.

**Analysis:** Since all the previous statements have been shown to be false, this statement is true. Therefore, the correct answer is that none of the above statements are true.

### Conclusion
The true statement among the options provided is: **None of these above.**

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