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1. Electric Charges and Fields
hard
Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $30^{\circ}$ with each other. When suspended in a liquid of density $0.8 \;g\, cm ^{-3}$, the angle remains the same. If density of the material of the sphere is $1.6\; g \,cm ^{-3}$, the dielectric constant of the liquid is
A
$2$
B
$1$
C
$4$
D
$3$
(AIEEE-2010)
Solution
From F.B.D of sphere, using Lami's theorem
$\frac{F}{m g}=\tan \theta$
when suspended in liquid, as $q$ remains same,
$\frac{F^{\prime}}{m g\left(1-\frac{\rho}{a}\right)}=\tan \theta$
$\frac{F}{m g}=\frac{F^{\prime}}{m g\left(1-\frac{\rho}{d}\right)} \text { where, } F^{\prime}=\frac{F}{K}$
$\frac{F}{m g}=\frac{F^{\prime}}{m g\left(1-\frac{\rho}{d}\right)}$
$K=\frac{1}{1-\frac{h}{h}}=2$
Standard 12
Physics
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