The lower plate of a parallel plate capacitor is supported on a rigid rod. The upper plate is suspended from one end of a balance. The two plates are joined together by a thin wire and subsequently disconnected. The balance is then counterpoised. Now a voltage $V = 5000\, volt$ is applied between the plates. The distance between the plates is $d =5\, mm$ and the area of each plate is $A = 100 cm^2.$ Then find out the additional mass placed to maintain balance…….$g$ [All the elements other than plates are massless and nonconducting] :-

Two capacitors of equal capacitance $(C_1 = C_2)$ are shown in the figure. Initially, while the switch $S$ is open, one of the capacitors is uncharged and the other carries charge $Q_0$. The energy stored in the charged capacitor is $U_0$. Sometimes after the switch is closed, the capacitors $C_1$ and $C_2$ carry charges $Q_1$ and $Q_2$, respectively; the voltages across the capacitors are $ V_1$ and $V_2$; and the energies stored in the capacitors are $U_1$ and $U_2$. Which of the following statements is INCORRECT ? 

The energy stored in the condenser is

Obtain the expression for the energy stored per unit volume in a charged capacitor.

A parallel plate capacitor of capacitance $2\; F$ is charged to a potential $V$. The energy stored in the capacitor is $E_1$. The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is $E _2$. The ratio $E _2 / E _1$ is