The centre of mass of a rigid body always lies inside the body, Is this statement true or false?

Explanation

To determine whether the statement "The centre of mass of a rigid body always lies inside the body" is true or false, we can analyze the concept of the center of mass (COM) and provide examples.

### Step-by-Step Solution:

1. **Understanding the Center of Mass**:
The center of mass 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 body can be considered to be concentrated for the purpose of analyzing translational motion.

2. **Analyzing the Statement**:
The statement claims that the center of mass always lies inside the rigid body. To evaluate this, we need to consider different shapes and distributions of mass.

3. **Examples of Rigid Bodies**:
- **Solid Sphere**: For a solid sphere, the mass is uniformly distributed throughout the volume, and the center of mass is located at the geometric center, which lies inside the sphere.
- **Ring**: In contrast, consider a thin ring. The mass is distributed along the circumference, and the center of mass is located at the center of the ring, which is outside the ring itself.

4. **Conclusion**:
Since we have found an example (the ring) where the center of mass lies outside the body, we conclude that the statement is false. The center of mass can lie both inside and outside the body depending on the shape and mass distribution.

### Final Answer:
The statement "The centre of mass of a rigid body always lies inside the body" is **false**.