As shown in the figure, the resistance of a galvanometer G can be found by the half-deflection method. Here the resistance R₂ is adjusted such that when the key K is closed the deflection in the galvanometer becomes half of the value as compared to when K is open. Half-deflection is obtained at R₂ = 4 $\Omega$ and thus the galvanometer resistance is found to be 6 $\Omega$. In this half-deflection condition the current (in mA) through the resistor R₁ is :

In a new system of units, the units of mass, length, time and current are $5 \mathrm{~kg}, 5 \mathrm{~m}, 5 \mathrm{~s}$ and 5 A , respectively. If $\mu_0$ and $\epsilon_0$ are the permeability and permittivity of free space, respectively, then in this new system of units, the magnitude of one SI unit of $\sqrt{\mu_0 / \epsilon_0}$, is :

A container of height 2 m , length 2 m and breadth 1 m is made of insulating vertical walls and two large area horizontal metal plates ( $\mathrm{M}_1$ and $\mathrm{M}_2$ ) which extend far beyond the vertical walls in all directions. The container is partitioned into two equal chambers with a thin insulating vertical wall. The partition wall contains a small hole of cross-sectional area $\sqrt{10} \mathrm{~cm}^2$ near its bottom edge. Initially the hole is closed and the left chamber of the container is completely filled with a liquid of dielectric constant $\epsilon_r=15$ and the right chamber is empty ( $\epsilon_r=1$ ). At time $t=0$, the hole is opened and the liquid flows from the left chamber to the right chamber. In both the chambers, the space above the liquid has $\epsilon_r=1$ and is maintained at atmospheric pressure. The schematic of the container at a time $t>0$ is shown in the figure.

[Given : acceleration due to gravity is $10 \mathrm{~ms}^{-2}$.]

The height (in m ) of the liquid in left chamber at $t=500 \mathrm{~s}$ is :

A container of height 2 m , length 2 m and breadth 1 m is made of insulating vertical walls and two large area horizontal metal plates ( $\mathrm{M}_1$ and $\mathrm{M}_2$ ) which extend far beyond the vertical walls in all directions. The container is partitioned into two equal chambers with a thin insulating vertical wall. The partition wall contains a small hole of cross-sectional area $\sqrt{10} \mathrm{~cm}^2$ near its bottom edge. Initially the hole is closed and the left chamber of the container is completely filled with a liquid of dielectric constant $\epsilon_r=15$ and the right chamber is empty ( $\epsilon_r=1$ ). At time $t=0$, the hole is opened and the liquid flows from the left chamber to the right chamber. In both the chambers, the space above the liquid has $\epsilon_r=1$ and is maintained at atmospheric pressure. The schematic of the container at a time $t>0$ is shown in the figure.

[Given : acceleration due to gravity is $10 \mathrm{~ms}^{-2}$.]

The difference in the capacitance (in F) between the metal plates at $t=0$ and that at $t=500 \mathrm{~s}$ is $(8-n) \epsilon_0$, where $\epsilon_0$ is the permittivity of free space. The value of $n$ is :