Note that, here the assumption is that mass is the continuous function of the volume. In the right picture of Fig.1, mass is not a continuous function of volume. In the limit, one may end up in a void.
Fig.1: Concept of continuum
This course will act as a foundation for fluid mechanics and solid mechanics courses. There, we deal with deformable bodies. In this course, we will be studying the behavior of rigid bodies under forces.
| Fundamentals of Engineering Mechanics |
CONTINUUM HYPOTHESIS A body consists of several particles. Each particle can be subdivided into molecules, atoms and electrons etc. It is not feasible to solve an engineering problem by treating a body as a congalomeration of such discrete particles. The body is assumed to consist of a continuous distribution of matter. In other words, body is treated as continuum. Fig. 1 illustrates this concept. The mass density |
at a point 
to the volume element ΔV enclosing the point , in the limit when 
tends to zero.