Question

Calculate amount of charge flow, when a conducting sphere of radius R and carrying a charge Q, is joined to an uncharged conducting sphere of radius 2R

Answer 1

at equilibrium, the potential of the two spheres are same.
Potential is directly proportional to charge/radius.
total charge of the combination=Q
Let us assume that a charge x flows between them

charge on larger sphere will be x and charge on smaller sphere will be Q - x

Potential on smaller sphere = k (Q - x) / R

Potential on larger sphere = k x /2R

Equating the potentials

k (Q - x) / R = k x /2R

Q - x = x/2

3x/2 = Q

x = 2Q/3

Thus a charge of 2Q/3 will flow between them