The centre of mass is a point in a system or object where its mass can be considered to be concentrated. It is the point where the entire mass of the object can be imagined to be concentrated, and the object would still behave the same way in terms of its motion.
The centre of mass and centre of gravity are often used interchangeably, but they are not exactly the same. The centre of mass is the point where the mass of an object is concentrated, while the centre of gravity is the point where the force of gravity on the object can be considered to act.
The centre of mass can be calculated by taking the average of the positions of all the particles or components of the object, weighted by their respective masses. Alternatively, it can also be calculated by balancing the object on a pivot point and marking the point where it balances.
The centre of mass is important in physics because it helps us understand the motion and stability of systems and objects. It is a useful concept in mechanics, as it can be used to calculate the overall motion of an object or system, and to determine whether it will remain in equilibrium or not.
No, the centre of mass does not always have to lie within the object. In some cases, such as a hollow sphere, the centre of mass may lie outside of the object. This is because the centre of mass is affected by the distribution of mass within the object, not just its physical boundaries.