A shower of protons from outer space deposits equal amounts of charge `+q` on the earth and the moon. The electrostatic repulsion then exactly counterbalances the gravitational attraction. Find the amount of charge q.

Explanation

Let the mass of the moon be `M_(m)` and that of the earth be `M_(e)` and the distance between them be `r`
The electrostatic repulsion between the moon and the earth
`=(qxxq)/(r^(2))=(q^(2))/(r^(2))`
Gravitational attraction `=(GM_(e)M_(m))/(r^(2))`
According to the question
`(q^(2))/(r^(2))=(GM_(e)M_(m))/(r^(2))` or `q=sqrt(GM_(e)M_(m))`