How far apart should two protons be if the electrical force of repulsion is equal to the weight (attraction to the earth) of one of the protons? (

Answer 1

The force between to protons is kq^2/r^2 (where k = 1/(4*pi*epislon_0))
This force equals mg, where m is the proton mass. So, you have

kq^2/r^2 = mg --> r^2 = kq^2/mg ---> r = q*sqrt(k/mg) ~ 11.9 cm