Four capacitors are connected to a battery as shown in the circuit. The ratio of charges on capacitors $C_2$ and $C_4$ is (Assume $C_1 = 1 \mu F, C_2 = 2 \mu F, C_3 = 3 \mu F, C_4 = 4 \mu F$ and the battery voltage $V = 10 \ V$ connected across the combination).

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: In electrostatics, a conductor does not store any net charge inside.
Reason $R$: Inside the capacitor (with no dielectric medium), the free charge carriers, if placed between the plates of capacitor, experience force and drift.
Choose the correct answer from the options given below:

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:

Show that for a combination of capacitors in series or parallel,the total energy stored is the sum of the energies stored in individual capacitors.

The potential differences that must be applied across the parallel and series combination of $3$ identical capacitors are such that the energy stored in them becomes the same. The ratio of the potential difference in the parallel combination to the series combination is:

$A$ fully charged capacitor of capacity $C$ is discharged through a small resistance wire embedded in a solid block of specific heat $s$ and mass $m$ under thermally isolated conditions. If the temperature of the block is raised by $\Delta T$,the initial potential difference across the capacitor is