Two identical charged spheres are suspended by strings of equal lengths .The string makes an angle of 30 with each other When suspended in liquid of density 0.8g/cm^3, The angle remains the same.if density of material of sphere is 1.6g/cm^3 the dielectric constant of liquid is?

Suppose T is the tension in the string . Force of repulsion  F=14πε0×q2r2
Resolving these forces in the horizontal and vertical components as shown in figure
  Tcosθ=mgTsinθ=14πε0×q2r2Dividing we get , tanθ=q24πε0mgr2 ---(1)On immersing in the liquid,Appearent weight mg' =mg1-0.81.6=mg2Force of repulsion F' = 14πε0K×q2r2If T' is the new tension ,then T'cosθ=mg2T'sinθ=q24πε0Kr2Dividing : tanθ=2q24πε0Kmgr2Using (1) 2q24πε0Kmgr2=q24πε0mgr2 K=2

Dielectric constant of liquid is 2

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