What should be the equal charge on helium-filled balloons as shown in the figure?

  • A
    $[\frac{mg r^2}{2k} \tan \theta]^{1/2}$
  • B
    $[\frac{2k}{mg r^2} \tan \theta]^{1/2}$
  • C
    $[\frac{mg r}{2k} \cot \theta]^{1/2}$
  • D
    $[\frac{2k}{mg r} \tan \theta]^{1/2}$

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Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting,massless strings of same length. At equilibrium,the angle between the strings is $\alpha$. The spheres are now immersed in a dielectric liquid of density $\rho_l = 800 \ kg \ m^{-3}$ and dielectric constant $K = 21$. If the angle between the strings remains the same after the immersion,then
$(A)$ electric force between the spheres remains unchanged
$(B)$ electric force between the spheres reduces
$(C)$ mass density of the spheres is $840 \ kg \ m^{-3}$
$(D)$ the tension in the strings holding the spheres remains unchanged

By using Coulomb's law,define unit charge.

$A$ charge $q$ is placed at the centre of the line joining two equal charges $Q$. The system of the three charges will be in equilibrium if $q$ is equal to:

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