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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 š›¼. The spheres are now immersed in a dielectric liquid of density 800 kg māˆ’3 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 māˆ’3

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 Tcos⁔α2=mgĀ andĀ Tsin⁔α2=FDividing,Ā tanα2=mgFAfter immersion in dielectric liquid, as given, there is no change in angle α  SoĀ Tcos⁔α2=mgāˆ’VρgĀ when ρ=800Kg/m3Ā andĀ Tsin⁔α2=Fer∓mgF=mgāˆ’VρgFer⇒1er=1āˆ’Ļdd=Ā density of sphere ⇒121=1āˆ’800d⇒d=840
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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 . The spheres are now immersed in a dielectric liquid of density 800 kg māˆ’3 and dielectric constant 21. If the angle between the strings remains the same after the immersion, then