Two identical charged spheres are suspended by strings of equal lengths. The string make an angle of 37 ° with each other. When suspended in a liquid of density 0 . 7 g cm - 3 , the angle remains same. If density of material of the sphere i

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Two identical charged spheres are suspended by strings of equal lengths. The string make an angle of 37 ° with each other. When suspended in a liquid of density 0 . 7 g cm - 3 , the angle remains same. If density of material of the sphere is 1 . 4 g cm - 3 , the dielectric constant of the liquid is _____ tan 37 ° = 3 4

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Correct answer: 0

For first case: T c o s θ = m g and T s i n θ = F e Therefore, t a n θ = F e m g t a n θ = F e ρ B V g . . . . ( i ) For second case: t a n θ = F e k ρ B V g - ρ L V g . . . . . ( ii ) From Eq. (i) & (ii), we get ρ B V g = ρ B - ρ L k V g ⇒ 1 . 4 = 0 . 7 k ⇒ k = 2

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