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
`tan15^@=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)/(in_r)` and the effective
gravitational force will become mg `(1-(rho_l)/rho_s)`

`mg_("eff")=mg[1-(rhoe)/(rhos)]`
Thus we have `tan15^@`
`=F/(mgin_r(1-(rho_l)/(rho_(s))))`
`in_r=(1)/(1-(rhol)/(rho_s))=2`