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...
What even *is* a particle in classical mechanics? 

Particles do exist in the real world, but their discovery pretty much made the invention of quantum mechanics necessary.

So to answer this question, you have to set up some straw man of a "classical mechanics particle" and then destroy that. For instance, we may pretend that atoms have the exact same properties as the bulk material, they're just for inexplicable reasons indivisible.

At this point, we cannot say any more whether particles do or do not exert forces on themselves. The particle might exert a gravitational force on itself, compressing it every so slightly. We could not detect this force, because it would always be there and it would linearly add up with other forces. Instead, this force would show up as part of the physical properties of the material, in particular its density. And in classical mechanics, those properties are mostly treated as constants of nature.