There are two uncharged identical metallic spheres 1 and 2 of radius r separated by a distance d (d > > r) . $\;\lambda\;$ charged metallic sphere of same radius having charge q is touched with one of the sphere . After some time it is moved away from the system . Now the uncharged sphere is earthed . Charge on earthed sphere is

Question

$(a)\;+\large\frac{q}{2}\qquad(b)\;-\large\frac{q}{2}\qquad(c)\;-\large\frac{qr}{2d}\qquad(d)\;-\large\frac{qd}{2r}$