# B What happen if i put r=0 into the formula F=(k)mm/r^2

1. Nov 17, 2016

### garylau

What happen if i put r=0 into the formula F=(k)mm/r^2
So 1/0=infinity ?

then F= infinite large in mathematical sense?
is that statement correct ?

thank

2. Nov 17, 2016

### BvU

That's what happens with the formula. In reality you can't have two masses in exactly one place, so the formula isn't endlessly applicable...

Mathematically you have a singularity.

3. Nov 17, 2016

### garylau

But In reality i can have two mass put in r=0.000001m
So the force still become very large?

4. Nov 17, 2016

### Math_QED

You cannot put in r = 0. That does not make sense. It does make sense to consider:

$\lim_{r \to 0}F = +\infty$. This means, intuitively, when $r$ approaches $0$, $F$ becomes larger and larger (F grows without bound).

5. Nov 17, 2016

### BvU

Well, the masses become smaller too for such small particles. One micron diameter with a reasonable density gives a very small mass !

On even smaller scales still other things happen. Protons, for example have a mass of only 1.67 10-31 kg and a diameter of 0.88 10-15 m. At such small scales other kinds of forces are much stronger.

6. Nov 17, 2016

### garylau

is it possible that the mass is very large but the r is very small?

7. Nov 17, 2016

### Demystifier

Yes. Moreover, in quantum physics mass is, in a certain sense, proportional to $1/r$.

8. Nov 17, 2016

### Staff: Mentor

Yes, then you get a very large force. But it is always finite. And if you want to put the masses too close, you have to consider quantum mechanics where the simple approach with a well-defined distance fails.