Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $37^{\circ}$ with each other. When suspended in a liquid of density $0.7 \text{ g/cm}^3$,the angle remains the same. If the density of the material of the sphere is $1.4 \text{ g/cm}^3$,the dielectric constant of the liquid is . . . . . . $\left(\tan 37^{\circ} = \frac{3}{4}\right)$.

If the distance between two point charges $+Q$ and $-Q$ is doubled,what will be the magnitude of the electrostatic force between them?

In the common crystal structure of $CsCl$,$Cs^+$ and $Cl^-$ ions are arranged in a $bcc$ structure as shown in the figure. The net electrostatic force on the $Cl^-$ ion due to the eight $Cs^+$ ions is .......

Two small spherical balls,each carrying a charge $Q = 10\,\mu C$ ($10$ micro-coulomb),are suspended by two insulating threads of equal lengths $1\,m$ each,from a point fixed in the ceiling. It is found that in equilibrium,the threads are separated by an angle of $60^o$ between them,as shown in the figure. What is the tension in the threads in $N$? (Given: $\frac{1}{4\pi \varepsilon_0} = 9 \times 10^9\,Nm^2/C^2$)

Four charges equal to $-Q$ are placed at the four corners of a square and a charge $q$ is at its centre. If the system is in equilibrium, the value of $q$ is

Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting,massless strings of same length. At equilibrium,the angle between the strings is $\alpha$. The spheres are now immersed in a dielectric liquid of density $\rho_l = 800 \ kg \ m^{-3}$ and dielectric constant $K = 21$. If the angle between the strings remains the same after the immersion,then
$(A)$ electric force between the spheres remains unchanged
$(B)$ electric force between the spheres reduces
$(C)$ mass density of the spheres is $840 \ kg \ m^{-3}$
$(D)$ the tension in the strings holding the spheres remains unchanged