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 protons are separated by a distance of $10^{-10} \ m$. If they are released,what will be their total kinetic energy at an infinite distance?

Six charges,three positive and three negative of equal magnitude,are to be placed at the vertices of a regular hexagon such that the electric field at $O$ is double the electric field when only one positive charge of the same magnitude is placed at $R$. Which of the following arrangements of charges is possible for $P, Q, R, S, T,$ and $U$ respectively?

$A$ thin spherical insulating shell of radius $R$ carries a uniformly distributed charge such that the potential at its surface is $V_0$. $A$ hole with a small area $\alpha 4 \pi R^2$ (where $\alpha \ll 1$) is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?

$A$ charged cork of mass $m$ suspended by a light string is placed in a uniform electric field of strength $E = (\hat{i} + \hat{j}) \times 10^5 \ NC^{-1}$ as shown in the figure. If in the equilibrium position,the tension in the string is $\frac{2mg}{(1 + \sqrt{3})}$,then the angle $\alpha$ with the vertical is:

Which of the following physical quantities have the same dimensions?