Two small identical balls carrying the charges of the same sign are suspended from the same point by insulating threads of equal length. When the surrounding space was filled with kerosene the divergence angle between the threads remained constant, What is the density of the material of which the balls are made ?

Explanation

In air the forces are as shown. In `K-oil`,
`F rarr F' = F//epsilon` and `mg rarr mg (1 - (rho_(0))/(rho))`,
Since the inclinations do not change
`(1)/(epsilon) = 1 - (rho_(0))/(rho)`
or, `(rho_(0))/(rho) = 1 - (1)/(epsilon) xx (epsilon - 1)/(epsilon)`
or, `rho = rho_(0) (epsilon)/(epsilon - 1)`
where `rho_(0)` in the density of K-oil and `rho` that of the material of which the balls are made.