(b) During the collision plates, α & β are together and hence must be at one potential. Suppose the charge on β is q1 and on γ is q2. Consider a point O. The electric field here must be zero.
Thus the charge on β and γ are Q + q/2 and q/2, respectively.
c) Let the velocity be v at the distance d after the collision. If m is the mass of the plate γ, then the gain in K.E. over the round trip must be equal to the work done by the electric field. After the collision, the electric field at γ is
The work done when the plate γ is released until the collision is F1d where F1 is the force on plate γ.
The work done after the collision till it reaches d is F2d where F2 is the force on plate γ.