Why do protons not fly apart under repulsion? I was given a problem where it was required to find the force of repulsion between 2 protons at largest separation inside a gold nucleus. The answer was around 1.2N. So, why doesn't this force of repulsion between the 2 protons cause them to fly apart?
 A: Welcome to stackexchange. Clearly the positively charged protons in a nucleus feel electromagnetic repulsion. It is the Strong Force that counters that and results in stable nuclei. The more nucleons, the more Strong Force. This is why heavier nuclei require more and more neutrons to counter the electromagnetic repulsion from the protons.
See also my answer to this question with a plot to show this.
A: If you let two protons approach each other, then there will be a repulsive electric force first. This can approach pretty big values. 1,2 (N) is pretty big for such a small mass. It would fly off (if let loose) with huge acceleration. If only the electric force was present. So there has to be another very strong force keeping them together. Once the protons have reached a certain (very small) distance, this strong force kicks in, but it will not fuse the protons. Therefore the electric repulsion is too big. Only in a neutron-proton environment, the strong force will be strong enough to keep the protons together. That's why no bound systems of two or more protons are found. The neutrons act as a kind of catalyzer.
In the sun when two protons fuse they will split again or one of them is transformed in a neutron, a neutrino, and a positron (with the same charge as a proton. This shows that there is another force. It's the weak force that induces this emission (alpha radiation). The neutron and proton can be held together by the strong force, but they first have to very close to one another. That's what the proton-proton fusion accomplishes.
