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Why protons do not repel each other in the nucleus of an atom ?

Nuclear force

The nuclear force (or nucleon–nucleon interaction or residual strong force) is the force between two or more nucleons. It is responsible for binding of protons and neutrons into atomic nuclei.

The force is powerfully attractive between nucleons at distances of about 1 femtometer (fm) between their centers

It rapidly decreases to insignificance at distances beyond about 2.5 fm.

At very short distances less than 0.7 fm, it becomes repulsive.

Nuclear force-distances

Interaction of nucleons through pion.

The model above shows a proton and neutron with overlapping pion fields, allowing the proton to donate a pion to the neutron, contributing to the nuclear force holding the two nucleons together.

The core of the nucleon which is surrounded by the pion cloud consists

of particles called quarks.

Quarks come in different types.

The proton and neutron are composed of three quarks of two different

types.

The proton is composed of two up-quarks and one down-quark and so

can be written: uud.

The neutron is composed of one up-quark and two down-quarks and so

can be written udd.

Nuclear Core structure

Interaction of nucleons mediated by pion-quark constituents.