Electrostatics Question 15
Question 15 - 2024 (30 Jan Shift 2)
Two identical charged spheres are suspended by string of equal lengths. The string make an angle of $37^{\circ}$ with each other. When suspended in a liquid of density $0.7 g / cm^{3}$, the angle remains same. If density of material of the sphere is $1.4 g / cm^{3}$, the dielectric constant of the liquid is $\left(\tan 37^{\circ}=\frac{3}{4}\right)$.
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Answer: (2)
$T \cos \theta=mg$
$T \sin \theta=F _e$
$\tan \theta=\frac{F _e}{mg}$
$\tan \theta=\frac{F _e}{\rho _B V g}$
$\tan \theta=\frac{F _e}{\frac{k}{\left(\rho _B-\rho _L\right) V g}}$.
From Eq. (i) $ \&$ (ii)
$\rho _B Vg=\left(\rho _B-\rho _L\right) kVg$
$1.4=0.7 k$
$k=2$
