Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $30^o$ with each other. When suspended in a liquid of density $1 \, g \, cm^{-3}$,the angle remains the same. If the density of the material of the sphere is $4/3 \, g \, cm^{-3}$,the dielectric constant of the liquid is:

Two equal negative charges $-q$ each are fixed at the points $(0, a)$ and $(0, -a)$ on the $Y$-axis. $A$ positive charge $Q$ is released from rest at the point $(2a, 0)$ on the $X$-axis. The charge $Q$ will :-

Two identical particles of mass $m$ carry a charge $Q$ each. Initially, one is at rest on a smooth horizontal plane and the other is projected along the plane directly towards the first particle from a large distance with speed $v$. The closest distance of approach is:

The dimension of $\frac{1}{2} \varepsilon_0 E^2$ (where $\varepsilon_0$ is the permittivity of free space and $E$ is the electric field) is:

Two particles each of mass $m$ and charge $q$ are separated by distance $r_1$ and the system is left free to move at $t = 0$. At time $t$,both the particles are found to be separated by distance $r_2$. The speed of each particle is

Two identical conducting spheres $A$ and $B$ carry equal charge. They are separated by a distance much larger than their diameter,and the force between them is $F$. $A$ third identical conducting sphere,$C$,is uncharged. Sphere $C$ is first touched to $A$,then to $B$,and then removed. As a result,the force between $A$ and $B$ would be equal to