The centre of mass of a body

Options

A. lies always at the geometrical centre
B. lies always inside the body
C. lies always outside the body
D. may lie within or outside the body

Answer

To solve the question regarding the location of the center of mass of a body, we will analyze the options given and understand the concept of the center of mass.

### Step-by-Step Solution:

1. **Understanding the 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 determined by the distribution of mass within the object.

2. **Analyzing the Options**:
- **Option A**: "Lies always at the geometrical center" - This is not true for all shapes. The geometrical center may not coincide with the center of mass, especially in irregular shapes.
- **Option B**: "Lies always inside the body" - This is also not true. There are cases where the center of mass can lie outside the physical boundaries of the body.
- **Option C**: "Lies always outside the body" - This is incorrect as well. Many objects have their center of mass located within their physical structure.
- **Option D**: "May lie within or outside the body" - This option is true. The center of mass can be located inside the body (like in a solid sphere) or outside the body (like in a hollow ring).

3. **Conclusion**:
- Based on the analysis, the correct answer is **Option D**: The center of mass of a body may lie within or outside the body.