Question: We all have elaborative discussion in physics about classical mechanics as well as interaction of particles through forces and certain laws which all particles obey.

I want to ask,Does a particle exert a force on itself?

**EDIT**

Thanks for the respectful answers and comments.I edited this question in order to make it more elaborated.

I just want to convey that I assumed the particle to be a standard model of point mass in classical mechanics. As I don't know why there is a minimum requirement of two particles to interact with fundamental forces of nature,in the similar manner I wanted to ask does a particle exerts a force on itself?

Answer: 
This question is never addressed by teachers, altough students start asking it more and more every year (surprisingly). Here are two possible arguments.

1. A particle is meant to have 0 volume. Maybe you're used to exert a force on yourself, but you are an extended body. Particles are points in space. I find it quite hard to exert a force on the same point. Your stating that the sender is the same as the receiver. It's like saying that one point is gaining momentum from itself! Because forces are a gain in momentum, after all. So how can we expect that some point increases its momentum alone? That violates the conservation of momentum principle.
2. A visual example (because this question usually arises in Electromagnetism with Coulomb's law):

$$\vec{F}=K \frac{Qq}{r^2} \hat{r}$$

If $r=0$, the force is not defined, what's more, the vector $\hat{r}$ doesn't even exist. How could such force "know" where to point to? A point is spherically symmetric. What "arrow" (vector) would the force follow? If all directions are equivalent...
This exact question is considered at the end of Jackson's (somewhat infamous) *Classical Electrodynamics*. I think it would be appropriate to simply quote the relevant passage:

> 
> In the preceding chapters the problems of electrodynamics have been
>  divided into two classes: one in which the sources of charge and
>  current are specified and the resulting electromagnetic fields are
>  calculated, and the other in which the external electromagnetic fields
>  are specified and the motions of charged particles or currents are
>  calculated...
> 
> 
> It is evident that this manner of handling problems in 
>  electrodynamics can be of only approximate validity. The motion of
>  charged particles in external force fields necessarily involves the
>  emission of radiation whenever the charges are accelerated. The
>  emitted radiation carries off energy, momentum, and angular momentum
>  and so must influence the subsequent motion of the charged particles.
>  Consequently the motion of the sources of radiation is determined, in
>  part, by the manner of emission of the radiation. A correct treatment
>  must include the reaction of the radiation on the motion of the
>  sources.
> 
> 
> Why is it that we have taken so long in our discussion of
>  electrodynamics to face this fact? Why is it that many answers
>  calculated in an apparently erroneous way agree so well with
>  experiment? A partial answer to the first question lies in the second.
>  There are very many problems in electrodynamics that can be put with
>  negligible error into one of the two categories described in the first
>  paragraph. Hence it is worthwhile discussing them without the
>  added and unnecessary complication of including reaction effects. The
>  remaining answer to the first question is that a completely
>  satisfactory classical treatment of the reactive effects of radiation
>  does not exist. The difficulties presented by this problem touch one
>  of the most fundamental aspects of physics, the nature of an
>  elementary particle. Although partial solutions, workable within
>  limited areas, can be given, the basic problem remains unsolved.
> 
> 
> 

There are ways to try to handle these self-interactions in the classical context which he discusses in this chapter, i.e. the Abraham-Lorentz force, but it is not fully satisfactory. 

However, a naive answer to the question is that really particles are excitations of fields, classical mechanics is simply a certain limit of quantum field theory, and therefore these self-interactions should be considered within that context. This is also not entirely satisfactory, as in quantum field theory it is assumed that the *fields* interact with themselves, and this interaction is treated only perturbatively. Ultimately there is no universally-accepted, non-perturbative description of what these interactions really are, though string theorists might disagree with me there.