Two charged spheres are suspended by strings of equal length. 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. The dielectric constant of the liquid is ........ (The density of the material of the sphere is $1.6 \ g/cm^3$.)

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

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 . . . . . . $\left(\tan 37^{\circ} = \frac{3}{4}\right)$.

An electron is moving around the nucleus of a hydrogen atom in a circular orbit of radius $r$. The Coulomb force $\vec{F}$ between the two is

Two electric charges $+q$ and $+q$ are placed at a distance $r$. The force between them is $F$. If one charge is fixed and the other moves in a circle of radius $r$,the work done will be .......

Three charges $q$,$Q$,and $4q$ are placed in a straight line of length $l$ at points distant $0$,$\frac{l}{2}$,and $l$ respectively from one end. In order to make the net force on $q$ zero,the charge $Q$ must be equal to