Two identically charged spheres are suspended by strings of equal length. The strings make an angle of `30^(@)` with each other. When suspended in a liquid of density `0.8 g// c c` the angle remains same. What is the dielectric constant of liquid. Density of sphere`=1.6 g//c c`

Explanation

When set up shown in figure is in air, we have `tan 15^(@)=F/(mg)` When set up is immersed in the medium as shown in figure, the electric force experienced by the ball will reduce and will be equal to `F/epsilon_(r)` and the effective graviational force will become `mg(1-rho_(l)/rho_(s))`
Thus we have `tan 15^(@)=(F)/(mg in_(r)(1-rho_(l)/rho_(s)))=(F)/(mg) rArr in_(r)=1/(1-rho_(l)/rho_(s))=2`