Two identical non - conducting solid spheres of same and charge are suspended in air form a common point by two non - conducing massless string of same length . At equilibrium the angle between the strings is `alpha`. The spheres are now immersed in a dielectric liquid of density `800 kg m^(-3)` and dielectric constant 21. If the angle between the spheres remains the same after the immersion , then

Options

A. electric force between the spheres reamins unchanged
B. electic force between the sphere reduce
C. mass density of the spheres is `840 kg m^(-3)`
D. the tension in the string holding the spheres remains unchanged

Answer

A,C

Explanation

`T sin theta = F " ", " " T cos theta = mg`
`tan theta = (F)/(mg) " "…..(1)`
As force between two charge bodies dodies don.t upon medium hence , the force between them remain same because the distance spheres is same .
When it is submerged in liquid then `T sin theta = (E)/(epsi_(r))`
`tan theta = (F)/(mg(1-(rho_(l))/(rho_(s))) epsi_(r) " "..........(2)`
Equating (1) &(2)
` 1 - (rho_(l))/(rho_(s)) = (1)/(epsi_(r)) , 1 - (800)/(rho_(s)) = (1)/(21)`
`rho_(s) = 840 kg//m^(3)`
` T = (T)/(epsi_(r)) = (T)/(21)`