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Charged spheres hung by threads keep the same angle when dipped in a liquid: dielectric constant of the liquid

The same question, asked 2 times: 30 Jan 2024*, 1 Feb 2024. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    30 Jan 2024

    117
    Two identical charged spheres are suspended by string of equal lengths. The string make an angle of 37∘37^{\circ} with each other. When suspended in a liquid of density 0.7 g/cm30.7\text{ }g/cm^{3}, the angle remains same. If density of material of the sphere is 1.4 g/cm31.4\text{ }g/cm^{3}, the dielectric constant of the liquid is _____ (tan⁡37∘=34)\left( \tan37^{\circ}=\frac{3}{4} \right).
  2. Question 2

    1 Feb 2024

    24
    Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle θ\theta with each other. When suspended in water the angle remains the same. If density of the material of the sphere is 1.5 g/cc1.5\text{ }g/cc, the dielectric constant of water will be ______ (Take density of water =1 g/cc= 1\text{ }g/cc )