In a liquid medium of dielectric constant K and of specific gravity 2, two identically charged spheres are suspended from a fixed point by threads of equal lengths. The angle between them is `90^(@)`. In another medium of unknown dielectric constant `K^(1)`, and specific gravity 4, the angle between them becomes `120^(@)`. If density of material of spheres is 8gm/cc then find `K^(1)`.

Explanation

To solve the problem, we need to analyze the forces acting on the charged spheres in both mediums and apply the principles of electrostatics and buoyancy.

### Step-by-step Solution:

1. **Understanding the Forces in Medium 1:**
- In the first medium, the two charged spheres create an electrostatic force that causes them to repel each other. The angle between the threads is 90 degrees.
- The electrostatic force \( F_e \) between the two spheres is given by:
\[
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