Question

Two identical conducting spheres carrying different charges attract each other with a force f when placed in a medium at a distance d apart the spheres are brought into contact and then taken to the original positions of the two spheres repel each other with a force whose magnitude is equal to that of the initial attractive force the ratio between initial charges on the spheres

Answer 1

Since the two charges (spheres) attract, they will be opposite in sign, ie, q1 and –q2.
Force, F= k * q1 * q2/ d2
After touching, charge on each will be (q1 - q2)/2.
New force, F=k*[(q1 - q2)/2]2/ d2.
Since both the force are same(given in question)
So, on solving by quadratic equations, we get
q1/ q2 = -(3 + √(8)) or (-3 + √(8))