If $L$ and $C$ are inductance and capacitance respectively,then the dimensional formula of $(LC)^{-\frac{1}{2}}$ is

In an oscillating $LC$ circuit,the total stored energy is $U$ and the maximum charge on the capacitor is $Q$. When the charge on the capacitor is $\frac{Q}{2}$,the energy stored in the inductor is:

The frequency of the output signal of an $LC$ oscillator circuit is $F \ Hz$ with a capacitance of $0.1 \ \mu F$. If the value of the capacitor is increased to $0.2 \ \mu F$,then the frequency of the output signal will be

$A$ $60\,\mu F$ capacitor is charged to $100\,V$. This charged capacitor is connected across a $15\,mH$ coil,so that $LC$ oscillations occur. The maximum current in the coil is:

Explain how $LC$ oscillations take place in the circuit.

Consider the following circuit. By keeping $S_1$ closed,the capacitor is fully charged and then $S_1$ is opened and $S_2$ is closed,then