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$[A]$ The electric flux passing through the curved surface of the hemisphere is $-\frac{\mathrm{Q}}{2 \varepsilon_0}\left(1-\frac{1}{\sqrt{2}}\right)$
$[B]$ Total flux through the curved and the flat surfaces is $\frac{Q}{\varepsilon_0}$
$[C]$ The component of the electric field normal to the flat surface is constant over the surface
$[D]$ The circumference of the flat surface is an equipotential

Statement $I$ : Electric potential is constant within and at the surface of each conductor.
Statement $II$ : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point.
In the light of the above statements, choose the most appropriate answer from the options give below.
Note: $V_{1,2,3,4}$ are the potential differences across $C_{1,2,3,4}$ and $Q_{1,2,3,4}$ are the final charges stored in $C_{1,2,3,4}$ respectively.

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($1$) Which one of the following statements is correct?
($A$) The balls will stick to the top plate and remain there
($B$) The balls will bounce back to the bottom plate carrying the same charge they went up with
($C$) The balls will bounce back to the bottom plate carrying the opposite charge they went up with
($D$) The balls will execute simple harmonic motion between the two plates
($2$) The average current in the steady state registered by the ammeter in the circuit will be
($A$) zero
($B$) proportional to the potential $V_0$
($C$) proportional to $V_0^{1 / 2}$
($D$) proportional to $V_0^2$
Give the answer quetion ($1$) and ($2$)