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Two identically charged pith balls are suspended from the some point by two massless identical threads density of each ball is $\rho $. If system is immersed in a medium of density $\sigma $, balls remain undeflected, then the dielectric constant of medium is
$\frac{\rho }{{\rho - \sigma }}$
$\frac{ \rho - \sigma }{{\rho }}$
$\frac{\sigma }{{\rho - \sigma }}$
$\frac{ \rho - \sigma }{{\sigma }}$
Solution
$\mathrm{T} \sin \theta=\mathrm{F}_{\mathrm{o}}$
$\mathrm{T} \cos \theta=\mathrm{mg}$
$\tan \theta=\frac{F_{0}}{m g}$
$\mathrm{F}_{0}=\operatorname{mg} \tan \theta$ ……….$(i)$
In medium
$\frac{\mathrm{F}_{0}}{\mathrm{K}}=\operatorname{mg}\left(1-\frac{\sigma}{\rho}\right) \tan \theta $ ………..$(ii)$
from $(i)$ and $(ii)$
$\mathrm{K}=\frac{\rho}{\rho-\sigma}$
