Two indentical pith balls, each carrying charge q, are suspended from a common point by two strings of equal length l. Find the mass of each ball if the angle between the strings is `2theta` in equilibrium.

Explanation

Let `x` be the separation between balls in equilibrium.
Each ball is in equilibrium under the action of the following forces:
(a) Weight of the ball , `mg`
(b) Repulsive electric force ,`F = (1)/(4 pi in_(0)) .(q^(2))/(x^(2))`
(c ) Tension in the string , `T`
Resolving `T` in the horizontal and vertical direction , since ball is in equilibrium
`T sin theta = F` (i)
`T cos theta = mg` (ii)
By (i)//(ii) , `tan theta = (F)/(mg) = ((1)/(4 pi in_(0)) (q^(2))/(x^(2)))/(mg)`
`(x)/(2) = l sin theta rArr x = 2 l sin theta`
`q^(2) = 4 pi in_(0) mg x^(2) tan theta`
`= 4 pi in_(0) mg (2l sin theta)^(2) tan theta`
`q = [ 16 pi in_(0) mgl^(2) sin^(2) theta tan theta]^(1/2)`