The capacitor of capacitance $C$ can be charged (with the help of a resistance R ) by a voltage source V , by closing switch $\mathrm{S}_1$ while keeping switch $\mathrm{S}_2$ open. The capacitor can be connected in series with an inductor L by closing switch $\mathrm{S}_2$ and opening $\mathrm{S}_1$.

If the total charge stored in the LC circuit.is $\mathrm{Q}_0$, then for $t \geq 0$,

If the level of liquid starts decreasing slowly when the level of liquid is at a height $h_1$ above the cylinder, the block just starts moving up. Then, the value of $h_1$ is:

Let the cylinder is prevented from moving up, by applying a force and water level is further decreased. Then, the height of water level ( $h_2$ in the figure) for which the cylinder remains in original position without application of force is

If the height $h_2$ of water level is further decreased, then