Q.

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

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a

mass density of the spheres is 840 kg m−3

b

electric force between the spheres reduces

c

the tension in the strings holding the spheres remains unchanged

d

electric force between the spheres remains unchanged

answer is A, C.

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Detailed Solution

The net electric force on any sphere is lesser but by Coulomb law the force due to one sphere to another remain the same.

Question Image

In equilibrium 

Tcosα2=mg and Tsinα2=F

Dividing, tanα2=mgF

After immersion in dielectric liquid, as given, there is no change in angle α 

 So Tcosα2=mgVρg when ρ=800Kg/m3 and Tsinα2=FermgF=mgVρgFer

1er=1ρdd= density of sphere 121=1800dd=840

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