Two identical charged spheres are suspended by string of equal le… - Vidyadip

Question

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 $..........\left(\tan 37^{\circ}=\frac{3}{4}\right)$.

✓

Answer

$(d)\ (2)$

$ T \cos \theta= mg$
$T \sin \theta= F _{ e }$
$\tan \theta=\frac{ F _{ e }}{ mg }$
$\tan \theta=\frac{F_{e}}{\rho_{B} V g}$
$\tan \theta=\frac{F_{e}}{\frac{k}{\left(\rho_{B}-\rho_{L}\right) Vg}}$
From Eq. $(i) \ (ii) $
$\rho_{B} Vg=\left(\rho_{B}-\rho_{L}\right) kVg$
$1.4=0.7 k$
$k=2$

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