Final answer:
The centre of gravity and the center of mass of an object coincide in a uniform gravitational field, where gravity is constant, typically equal to 9.8 m/s² on Earth. This allows the object to undergo translational motion without rotation when a force is applied at this point.
Step-by-step explanation:
The centre of gravity and the center of mass of an object coincide when the gravitational field in which the object is located is uniform. This is because the center of mass is defined as the average location of the total mass of an object, and it is the point where the entire mass of the object can be considered to be concentrated for the analysis of translational motion. When the gravitational field is non-uniform, the two points may not coincide because the weight force acts differently on different parts of the object. However, for most practical situations on Earth, the gravitational field is uniform enough that the acceleration due to gravity (g = 9.8 m/s²) is constant throughout the object, making the center of gravity and center of mass identical.
Moreover, during linear momentum and collision events, it's highlighted that the center of mass functions as a crucial reference point for predicting the motion of the system. This holds true for both one-dimensional and two-dimensional collisions where momentum is conserved. In Newtonian physics, for any type of object in equilibrium or undergoing a force, understanding the center of mass is foundational, since it's where a force can be applied to cause pure translational motion without rotation.