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 + sqrt8)` only
B. `(3 - sqrt8)` only
C. `(3 + sqrt8)` or `(3 - sqrt8)`
D. `+sqrt3`

Answer

C

Explanation

`F_1=1/(4piepsilon_0).(Q_1Q_2)/d^2 and F_2 =1/(4piepsilon_0)(((Q_1-Q_2)/2)^2)/d^2`
Given `F_1 -F_2`
`implies Q_1Q_2 = (((Q_1-Q_2)/2)^2)/d^2`
`implies 4Q_1Q_2 =Q_1^2+Q_2^2-2Q_1Q_2`
`impliesQ_1^2+Q_2^2-6Q_1Q_2=0implies (Q_1/Q_2)^2 +1-6(Q_1/Q_2)=0`
`Q_1/Q_2 = (6pmsqrt((36-4)))/(2) =3pmsqrt8`
`Q_1/Q_2 = 3 + sqrt8` or `3-sqrt8`