Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $30^{\circ}$ with each other. When suspended in a liquid of density $0.8 \; g \, cm^{-3}$,the angle remains the same. If the density of the material of the sphere is $1.6 \; g \, cm^{-3}$,the dielectric constant of the liquid is:

Two identical charged spheres are suspended from a common point by two massless strings of length $l$. Initially,they are at a distance $d$ $(d << l)$ due to mutual repulsion. The charge begins to leak from both spheres at a constant rate. As a result,the spheres approach each other with a velocity $v$. Then,the velocity $v$ as a function of the distance $x$ between them is:

$A$ tiny spherical oil drop carrying a net charge $q$ is balanced in still air with a vertical uniform electric field of strength $\frac{81 \pi}{7} \times 10^5 \text{ Vm}^{-1}$. When the field is switched off,the drop is observed to fall with a terminal velocity $2 \times 10^{-3} \text{ ms}^{-1}$. Given $g = 9.8 \text{ ms}^{-2}$,viscosity of the air $\eta = 1.8 \times 10^{-5} \text{ Ns m}^{-2}$,and the density of oil $\rho = 900 \text{ kg m}^{-3}$,the magnitude of $q$ is:

Four charges $2C, -3C, -4C$ and $5C$ respectively are placed at the corners of a square of side length $L$. Which of the following statements is true for the point of intersection of the diagonals?

$A$ pendulum bob of mass $30.7 \times 10^{-6} \, kg$ and carrying a charge $2 \times 10^{-8} \, C$ is at rest in a horizontal uniform electric field of $20000 \, V/m$. The tension in the thread of the pendulum is $(g = 9.8 \, m/s^2)$.

Two identical metal spheres charged with $+12 \mu C$ and $-8 \mu C$ are kept at a certain distance in air. They are brought into contact and then kept at the same distance. The ratio of the magnitudes of electrostatic forces between them before and after contact is (in $: 1$)