A circuit consists of a coil with inductance $L$ and an uncharged capacitor of capacitance $C$. The coil is in a constant uniform magnetic field such that the flux through the coil is $\varphi$.  At time $t=0$, the magnetic field is abruptly switched off. Let ${\omega }_0=\frac{1}{\sqrt{LC}}$ and ignore the resistance of the circuit. Then, $$ 

Consider the configuration of a stationary water tank of cross-section area $A_0$ and a small bucket as shown in figure. $$

What should be the speed, $v$ of the bucket so that the water leaking out of a hole of cross-sectional area $A$ (as shown) from the water tank does not fall outside the bucket? Take $h=5 \mathrm{m}\text{, }H=5 \mathrm{m}\text{,} g=10 \mathrm{m} {\mathrm{s}}^{-2}$, $A=5 {\mathrm{cm}}^2$ and $A_0=500 {\mathrm{cm}}^2$.

The circuit below is used to heat water kept in a bucket.

Assume heat loss only by Newton's law of cooling, the variation in the temperature of the water in the bucket as a function of time is depicted by,