How do I calculate the ratio of charges for metal sphere?

[eureka_beyond]

Homework Statement

here's how the question goes:
the magnitudes of the charges on two identical small metal spheres are in the ratio 5:1. the coulomb interaction force between them is F1. if they are brought into contact and then separated to their respective original positions, the coulomb interaction force between them becomes F2. Which of the following are possible magnitudes of F1 : F2
a) 5:9
b)5:4
c)5:2

the correct answer for this question is a) and b), leaving c) incorrect

Homework Equations

coulomb's law:
F= kq1q2/r2

The Attempt at a Solution

I assume that the spheres carry 5x and x charge originally. So by coulonmb's law,
F1= k(5x)(x)/r2. After the spheres touch each other, their charges are share equally, so each of them will now have a charge of 3x. Hence, F2=k(3x)(3x)/r2. After some simplification, the ratio of F1:F2 should be 5:9. Which is the answer to a) . So I understand a), it's b) and c) that I don't understand.
furthermore, are charges always equally share? (like what I assume it to be in my attempt? or did I do something wrong?) If charges don't always have to be eqally share, even for identical spheres, then shouldn't both b) and c) be correct? (base on by guessing only)
thanks

 

[vishal007win]

you just assumed charges to be of same sign, what if one is positive and one is negative?

 

[eureka_beyond]

oh right! so that's where 4 comes from. thanks. okay, so this means that charges do share equally between identical spheres. Do charges share eqally if they're not identical?

 

[vishal007win]

no if they are not identical , charge will not be distributed equally,
Its the potential that becomes equal,
V=q/C
so if capacitance of both spheres is equal then charges shared will be equal, but if it is not the case, distribution will be uneven.