Two identical balls each having a density `rho` are suspended from a common point by two insulating string of equal length. Both the balls have equal mass and charge. In equilibrium each string makes an angle `theta` with vertical. Now, both the balls are immersed in a liquid. As a result the angle `theta` does not change. The density of the liquid is `sigma`. find the dielectric constant of the liquid.

Explanation

Let V be the volume of each ball, then the mass of each ball is `m=propV`.When the balls are in air, from the previous problem.
`F=mg tan theta=rhoV g tan theta`...(i)
,
when the balls are suspended in liquid, the Coulombic force is reduced to `F'=F//K` and apparent weight=weight -upthrust, i.e
`W' = rhoVg-sigmaVg`
According to the problem, angle `theta`is unchanged therefore.
`F'=W' tan theta=(rho Vg- sigmaVg) tan theta` ...(ii)
From Eqs, (i) and (ii) we get
`(F)/(F')=K=(rhoVg)/(rhoVg-sigmaVg)=(rho)/(rho-sigma)`.