Three identical charged balls each of charge 2 C are suspended from a common point P by silk threads of 2 m each (as shown in figure). They form an equilateral triangle of side 1m.
The ratio of net force on a charged ball to the force between any two charged balls will be :

Solution

Physics sir · 3 steps

Each ball feels two equal Coulomb pushes 60° apart; add them as vectors, not as plain numbers.

1. One pair. Any two balls are 1 m apart with 2 C each, so every pair repels with the same force F = k(2)(2)/1² = 4k. The thread length of 2 m does not change this.
2. Angle between forces. Take ball B₁. It is pushed away from B₂ and away from B₃. Both pushes have size F, and since the balls form an equilateral triangle, the angle between them is 60°.

   Fₙₑₜ = √(F² + F² + 2F²cos 60°) = √3 F

3. So. The net electrostatic force on a ball divided by the force between two balls is √3F : F = √3 : 1, which is option (d).

The idea to keep. Two equal forces F at an angle θ add up to 2F cos θ/2. In an equilateral triangle θ = 60°, so the resultant is always √3F.

Answer from the NTA final answer key. Solution by PrepWiser.