A) \[\sqrt{LC}\]
B) \[\pi \sqrt{LC}\]
C) \[\frac{\pi }{4}\sqrt{LC}\]
D) \[2\pi \sqrt{LC}\]
Correct Answer: C
Solution :
\[q={{q}_{0}}\cos \omega \,t\]energy is halved when \[q=\frac{{{q}_{0}}}{\sqrt{2}}\] \[\Rightarrow \omega \,t=\frac{\pi }{4}\] \[\Rightarrow \,\frac{1}{\sqrt{LC}}t=\frac{\pi }{4}\] \[\Rightarrow \,t=\frac{\pi }{4}\sqrt{Lc}\]
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