Question

Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is r, Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now become.

$open parentheses fraction numerator 1 over denominator square root of 2 end fraction close parentheses squared$
$open parentheses fraction numerator straight r over denominator 3 square root of 2 end fraction close parentheses$
$open parentheses fraction numerator 2 straight r over denominator square root of 3 end fraction close parentheses$
$open parentheses fraction numerator 2 straight r over denominator 3 end fraction close parentheses$

Solution

open parentheses fraction numerator straight r over denominator 3 square root of 2 end fraction close parentheses

As F_e =mg tanθ
We have F_e =tan θ₁ ad F'_e = tan θ
therefore,
$fraction numerator straight F subscript straight e apostrophe over denominator straight F subscript straight e space end fraction space equals space fraction numerator tan space straight theta subscript 1 over denominator tan space straight theta subscript 1 end fraction$