How are protons present in the nucleus if both have the same charge?

The protons repel each other because they have the same electrical charge.
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However, that is not the only force in the nucleus. All protons repel each other due to their electrical charge. All protons and neutrons attract each other due to the strong nuclear force. So although every proton repels every other proton, protons and neutrons attract other protons and neutrons due to the strong nuclear force. In addition, the strong nuclear force is, well, strong. It is much, much stronger than the electrical repulsion.
However, the strong nuclear force is very short range. It is so short range that it can’t attract other nucleons (protons and neutrons) on the opposite side of the nucleus. (Now that’s short range.) But each proton can still repel every other proton. Therefore, when an atom gets much larger than about neon, the nucleus needs more neutrons than protons to be stable. The situation become worse as the nucleus gets larger. When you get up to lead, there are almost 50% more neutrons than protons. That is necessary to overcome the electrical repulsion.

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