Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 3 0 ∘ with each other. When suspended in a liquid of density 0.8 g cm − 3 , the angle remains the

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Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 3 0 ∘ with each other. When suspended in a liquid of density 0.8 g cm − 3 , the angle remains the same. If density of the material of the sphere is 16 g cm − 3 , the dielectric constant of the liquid is

TestHub · Accepted Answer

From F.B.D of sphere, using Lami's theorem $\frac{F}{mg} = tan θ$ when suspended in liquid, as $θ$ remains same, $∴ \frac{F ^{'}}{mg ( 1 - \frac{ρ}{d} )} = tan θ$ using (i) and (ii) $\frac{F}{m g} = \frac{F ^{'}}{m g ( 1 - \frac{ρ}{d} )} where, F^{'} = \frac{F}{K}$ $∴ \frac{F}{mg} = \frac{F ^{'}}{mg K ( 1 - \frac{ρ}{d} )}$ or $K = \frac{1}{1 - \frac{ρ}{d}} = 2$

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