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 š¼. The spheres are now immersed in a dielectric liquid of density 800 kg mā3 and dielectric constant 21. If the angle between the strings remains the same after the immersion, then
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a
electric force between the spheres remains unchanged
b
electric force between the spheres reduces
c
mass density of the spheres is 840 kg mā3
d
the tension in the strings holding the spheres remains unchanged
answer is A.
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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.In equilibriumĀ Tcosā”α2=mgĀ andĀ Tsinā”α2=FDividing,Ā tanα2=mgFAfter immersion in dielectric liquid, as given, there is no change in angle α  SoĀ Tcosā”α2=mgāVĻgĀ whenĀ Ļ=800Kg/m3Ā andĀ Tsinā”α2=Ferā“mgF=mgāVĻgFerā1er=1āĻdd=Ā density of sphereĀ ā121=1ā800dād=840
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