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 density of the material of the sphere is $1.6\; g \,cm ^{-3}$, the dielectric constant of the liquid is

A point charge of $40$ stat coulomb is placed $2$ $cm$ in front of an earthed metallic plane plate of large size. Then the force of attraction on the point charge is.....$dynes$

A simple pendulum of period $T$ has a metal bob which is negatively charged. If it is allowed to oscillate above a positively charged metal plate, its period will

Two identical conducting spheres, having charges of opposite sign, attract each other with a force of $0.108$ $N$ when separated by $0.5$ $m$. The spheres are connected by a conducting wire, which is then removed, and thereafter, they repel each other with a force of $ 0.036$ $N$. The initial charges on the spheres are

Two identical conducting spheres carry identical charges. If the spheres are set at a certain distance apart, they repel each other with a force $F$. A third conducting sphere identical to the other two, but initially uncharged is touched to one sphere and then to the other before being removed. The force between the original two spheres is now

A charge $q$ is placed at the centre of the line joining two equal charges $Q$. The system of the three charges will be in equilibrium, if $q$ is equal to