Two identically charged pith balls are suspended from the some po… - Vidyadip

MCQ

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

✓
$\frac{\rho }{{\rho - \sigma }}$
B
$\frac{ \rho - \sigma }{{\rho }}$
C
$\frac{\sigma }{{\rho - \sigma }}$
D
$\frac{ \rho - \sigma }{{\sigma }}$

✓

Answer

Correct option: A.

$\frac{\rho }{{\rho - \sigma }}$

a
$\mathrm{T} \sin \theta=\mathrm{F}_{\mathrm{o}}$

$\mathrm{T} \cos \theta=\mathrm{mg}$

$\tan \theta=\frac{F_{0}}{m g}$

$\mathrm{F}_{0}=\operatorname{mg} \tan \theta$ ..........$(i)$

In medium

$\frac{\mathrm{F}_{0}}{\mathrm{K}}=\operatorname{mg}\left(1-\frac{\sigma}{\rho}\right) \tan \theta $ ...........$(ii)$

from $(i)$ and $(ii)$

$\mathrm{K}=\frac{\rho}{\rho-\sigma}$

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