A parallel plate capacitor whose capacitance $C$ is $14\, pF$ is charged by a battery to a potential difference $V =12\, V$ between its plates. The charging battery is now disconnected and a porcelin plate with $k =7$ is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of $..........pJ$. (Assume no friction)
A$872$
B$972$
C$784$
D$864$
JEE MAIN 2021, Medium
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D$864$
d $U _{ i }=\frac{1}{2} \times 14 \times 12 \times 12 pJ \quad\left(\because U =\frac{1}{2} CV ^{2}\right)$
$=1008 pJ$
$U _{ f }=\frac{1008}{7} pJ =144 pJ \quad\left(\because C _{ m }= k C _{0}\right)$
Mechanical energy $=\Delta U$
$=1008-144$
$=864 pJ$
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