$512$ identical drops of mercury are charged to a potential of $2\, V$ each. The drops are joined to form a single drop. The potential of this drop is ......... $V.$
JEE MAIN 2021, Diffcult
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$Q =512 q$
Volume $_{i}=$ Volume $_{f}$
$512 \times \frac{4}{3} \pi r^{3}=\frac{4}{3} \pi R^{3}$
$2^{9} r ^{3}= R ^{3}$
$R =8 r$
$2=\frac{ kq }{ r }$
$V =\frac{ kQ }{ R }=\frac{ k 512 q }{8 r }$
$V =128$
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($1$) Which one of the following statements is correct?
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($B$) 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
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($A$) zero
($B$) proportional to the potential $V_0$
($C$) proportional to $V_0^{1 / 2}$
($D$) proportional to $V_0^2$
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