Question

What holds the nucleus together?

Answer 1

The Strong Nuclear Force.

Explanation:

There are four fundamental forces in the universe:
The Electromagnetic Force, Gravity, the Strong Nuclear Force, and the Weak Nuclear Force.

In the nucleus, you would expect that due to the electromagnetic force, all the protons would be repelling each other and separating. The electromagnetic force is much stronger than gravity, so would easily be able to overcome those attractive forces.
It is in fact the strong nuclear force which holds the nucleus together, and it also even holds the quarks which make up the nucleons together.