Repulsion between closely packed protons in the nucleus is overcome by

Strong nuclear force

Explanation:

As we know that positive charges repel each other so protons do repel each other although atoms are stable because of strong nuclear force acting between nucleons (protons and neutrons in nucleus are called nucleons) which overcome the repulsive force between the proton. Strong nuclear force is very short-range force and acts only in distance of angstrom or picometre.

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