The centre of mass of a body:*1 pointLies always at the geometrical centreLies always inside the bodyLies always outside the bodyMay lie within or outside the body

The centre of mass of a body may lie within or outside the body.

Here's why:

1. The center of mass is the point in an object where all of its mass can be considered to be concentrated.

2. For a uniform density object, the center of mass does indeed lie at the geometric center. This is because the mass is evenly distributed throughout the object.

3. However, for objects with irregular shapes or variable density, the center of mass may not be at the geometric center. It could be located anywhere in the space occupied by the object, depending on the distribution of mass.

4. Furthermore, for a system of particles (like a solar system), the center of mass may actually lie outside any of the individual particles.

So, the center of mass of a body may lie within or outside the body, depending on the distribution of mass.