Coulomb Law and Gravitation

Question

So today I was solving a problem from my book. I even did not understand it. I saw the solution but even did not understand the solution, The question is,

"In 1959 Lyttleton and Bondi suggested that the expansion of the Universe could be explained if matter carried a net charge. Suppose that the Universe is made up of hydrogen atoms with a number density $N$, which is maintained a constant. Let the charge on the proton be: $ep = – (1 + y)e$ where $e$ is the electronic charge. (a) Find the critical value of $y$ such that expansion may start."

It was given in the solution that expansion starts if coulomb repulsion on a hydrogen atom, at $R$, is larger than gravitational attraction. Why does this gravitational attraction come into play? Also could someone explain me the question and solution thoroughly?

Answer 1

See what you are missing here is that a charge both has a mass and a charge. Due to mass, it experiences an attractive gravitational force and due to its charge, it experiences a repulsive electric force.

Suppose you have only two Hydrogen atoms. As suggested in question you need to take protonic charge as greater than electronic charge. Due to this the molecule contains a net charge (protonic - electronic) and hence the two atoms repel. If this repulsion is greater than their gravitational force, they will start moving away.

Try doing this using simple logic and Newton's Second Law.