Centre of Mass:

The centre of mass/gravity of a body or a system of the particles is resultant of the weights of the individual particles making up the body or system. The center of mass of a body or a system of bodies is point which moves as though all of the mass were concentrated there and all the external forces were applied there.

Uniform Bodies

A uniform body is a body whose density is same throughout the body. By finding the centre of mass of the uniform bodies is straightforward relatively.

A lamina is 2-dimensional object. Or we can day that, it is a flat object whose thickness we can ignore.

If the body has a line of symmetry, the centre of mass/gravity will lie on this line. This is quite useful fact. The center of mass of a body does not coincide generally with its geometric center, and the property of it can be exploited. The engineers try to design a sports car's center of mass as low as possible to handle the car better.  For instance, the centre of mass of the circular lamina is at centre of the circle, as the centre of mass is on each axis of symmetry and they all meet at centre. The study of motion is restricted up to this point. We referred particle, object and body in one and same way. We considered that actual 3 dimensional rigid bodies moved so that all the constituent particles had same motion that is same trajectory, velocity and acceleration.The term center of mass is used often interchangeably with the center of gravity, but they are different physical concepts. They happen to coincide in the uniform gravitational field, but the gravity is not uniform; center of gravity refers to mean location of the gravitational force working on a body

The actual body, however, can move differently to the simplified paradigm. Consider a ball rolling down the incline plane or consider a stick thrown in the air. Different parts of body have different motions. While translating in the air, stick rotates about the moving axis.