Consider the circuit diagram as shown in the figure. The source has a voltage $V=V_0 \sin \omega t$. Both the resistors $A$ and $B$ have the same resistance. The capacitor and the inductor have capacitance $C$ and inductance $L$, respectively. For some frequency $\omega$, and certain initial charge in the capacitor, the current through the resistor $A$ is in phase with the source. What is the value of $\omega$ ?

A conducting wire carrying a steady current $I$ is shaped as shown in the figure below. All connected graight segments meet at right angles. What is the magnetic moment of the current loop?

Consider the shown circuit. The capacitors $C_1$ and $C_2$ have capacitances $2 \mu \mathrm{~F}$ and $8 \mu \mathrm{~F}$, respectively. The switch can connect point $X$ to either $Y$ or $Z$. Initially $X Y$ is connected until the capacitor is fully charged by the battery. Then the switch connects $X$ and $Z$, and the final charges on Cl and C 2 are $Q_1$ and $Q_2$, respectively. What is the value of the ratio $\frac{Q_2}{Q_1+Q_2}$ ?

Atomic masses of two oxygen isotopes ${ }_8^{16} \mathrm{O}$ and ${ }_8^{18} \mathrm{O}$ are 15.99491 u and 17.99916 u , respectively, where $u$ is the atomic mass unit. Masses of protom and neutron are given by 1.00727 u and I .00866 u , respectively. The speed of light is c . What is the difference between the binding energies of ${ }_8^{18} \mathrm{O}{ }_8^{16} \mathrm{O}$ nuclei in units of $u c^2$ ?