A GOOD QUESION made by me

A highly expected question made by me with a GREAT mind
The figure shows two capacitors of capacitance C and charge Q1 and Q2 respectively as shown in the figure.An uniform electric field E exists b/w the plates of the capacitors in the direction as shown in the figure.
A charged particle of mass m is projected with an initial velocity v as shown. THe charged particle enters the redion b/w the paltes and makes n no. of collisions with either of the plates as shown.The coefficient of resitution b/w the charged particle and the pate is e.
The charged particle leaves the region b/w the plates with velocity V'.
Find:-
(a) The relation b/w v and v'.
(b)The no. of collisions , n, of the charged particle with either of theplates.

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