Two identically charged pith balls are suspended from the some point by two massless identical threads density of each ball is $\rho $. If system is immersed in a medium of density $\sigma $, balls remain undeflected, then the dielectric constant of medium is

Two charges each of magnitude $Q$ are fixed at $2a$ distance apart. A third charge ($-q$ of mass $'m'$) is placed at the mid point of the two charges; now $-q$ charge is slightly displaced perpendicular to the line joining the charges then find its time period

Force between two identical spheres charged with same charge is $F$. If $75\%$ charge of one sphere is transfered to the other sphere then the new force will be

Four point charges, each of $+ q$, are rigidly fixed at the four corners of a square planar soap film of side ' $a$ ' The surface tension of the soap film is $\gamma$. The system of charges and planar film are in equilibrium, and $a=k\left[\frac{q^2}{\gamma}\right]^{1 / N}$, where ' $k$ ' is a constant. Then $N$ is

The diagrams depict four different charge distributions. All the charged particles are at same distance from origin $(i.e. OA = OB = OC = OD)$ $F_1$ , $F_2$ , $F_3$ and $F_4$ are the magnitude of electrostatic force experienced by a point charge $q_0$ kept at origin in figure $-1$ , figure $-2$ , figure $-3$ and figure $-4$ respectively. Choose the correct statement.

For regular pentagon system shown in figure, find force on $q_0$