An $\alpha$ particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by the above two particles will be:

Three identical capacitors $C_1, C_2$ and $C_3$ have a capacitance of $1.0 \mu F$ each and they are uncharged initially. They are connected in a circuit as shown in the figure and $C_1$ is then filled completely with a dielectric material of relative permittivity $\varepsilon_{r}$. The cell electromotive force (emf) $V_0=8 \,V$. First the switch $S_1$ is closed while the switch $S_2$ is kept open. When the capacitor $C_3$ is fully charged,$S_1$ is opened and $S_2$ is closed simultaneously. When all the capacitors reach equilibrium,the charge on $C_3$ is found to be $5 \mu C$. The value of $\varepsilon_{r}$ is:

Each capacitor shown in the figure has a capacitance of $5.0 \ \mu F$. The battery has an $emf$ of $50 \ V$. If the switch $S$ is closed,what amount of charge will flow through $AB$?

The plates $S$ and $T$ of an uncharged parallel plate capacitor are connected across a battery. The battery is then disconnected and the charged plates are now connected in a system as shown in the figure. The system shown is in equilibrium. All the strings are insulating and massless. The magnitude of charge on one of the capacitor plates is: [Area of plates = $A$]

$A$ capacitor of capacitance $C = 900 \, pF$ is charged fully by a $100 \, V$ battery as shown in figure $(a)$. Then it is disconnected from the battery and connected to another uncharged capacitor of capacitance $C = 900 \, pF$ as shown in figure $(b)$. The electrostatic energy stored by the system in figure $(b)$ is $\dots \times 10^{-6} \, J$.

When two identical capacitors are charged individually to different potentials and connected in parallel to each other,after disconnecting them from the source: