Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 37° with each other. When suspended in a liquid of density 0.7 g/cm³, the angle remains same. If density of material of the sphere is 1.4 g/cm³, the dielectric constant of the liquid is _______ (tan 37° = 3/4) Numerical answer type. Work it out, then open the answer.

Answer: 2. Same angle in air and liquid: F/mg = (F/K)/(mg(1 - σ/ρ)) ⇒ K = (ρ)/(ρ - σ). K = (1.4)/(1.4 - 0.7) = 2 Dielectric constant of the liquid = 2.

Two identical charged spheres are suspended by strings of equal… | JEE Main 2024 (30 Jan, Shift 2)

Q35JEE Main 2024 · 30 JAN · SHIFT 2Medium

Electric Charge & Coulomb's Law

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $37^\circ$ with each other. When suspended in a liquid of density $0.7\text{ g/cm}^{3}$ , the angle remains same. If density of material of the sphere is $1.4\text{ g/cm}^{3}$ , the dielectric constant of the liquid is _______ $\left(\tan 37^\circ = \frac{3}{4}\right)$

Numerical answer type. Work it out, then open the answer.

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Answer: 2

Same angle in air and liquid: $\dfrac{F}{mg} = \dfrac{F/K}{mg(1 - \sigma/\rho)} \Rightarrow K = \dfrac{\rho}{\rho - \sigma}$ .
$K = \dfrac{1.4}{1.4 - 0.7} = 2$
Dielectric constant of the liquid $= 2$ .

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