Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 30° 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 1.6 g cm⁻³, the dielectric constant of the liquid is (a) 4 (b) 3 (c) 2 (d) 1

Answer: (c). In air tan θ = F/mg. In the liquid force becomes F/K and effective weight mg(1 - (σ)/(ρ)). Same angle: K = (1)/(1 - σ/ρ) = (ρ)/(ρ - σ) K = (1.6)/(1.6 - 0.8) = 2 So the answer is (c) 2.

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Electric Charge & Coulomb's Law

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $30^\circ$ with each other. When suspended in a liquid of density $0.8\text{ g cm}^{-3},$ the angle remains the same. If density of the material of the sphere is $1.6\text{ g cm}^{-3},$ the dielectric constant of the liquid is

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Answer: (c)

In air $\tan\theta = \dfrac{F}{mg}$ . In the liquid force becomes $\dfrac{F}{K}$ and effective weight $mg\left(1 - \dfrac{\sigma}{\rho}\right)$ .
Same angle: $K = \dfrac{1}{1 - \sigma/\rho} = \dfrac{\rho}{\rho - \sigma}$
$K = \dfrac{1.6}{1.6 - 0.8} = 2$
So the answer is (c) 2.

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