Two identical conducting sphere carrying different charges attract each other with a force F when placed in air medium at a distance `d` apart. The spheres are brought into contact and then taken to their original positions. Now, the two sphere repel each other with a force whole magnitude is equal to the initial attractive force. The ratio between initial charges on the spheres is

Options

A. `-(3+sqrt(8))` only
B. `-3+sqrt(8)` only
C. `-(3+sqrt(8))` or `(-3+sqrt(8))`
D. `-sqrt(8)`

Answer

C

Explanation

`F=(Kq_(1)q_(2))/(d^(2))`
After touching `F.-K/(d^(2))((q_(1)+q_(2))^(2))/2`
`F=F.`
`q_(1)q_(2)=((q_(1)-q_(2))/2)^(2)`
`(q_(1))/(q_(2))=-3+sqrt(8)` or `-3-sqrt(8)`