Two identical non - conducting solid spheres of same mass and charge are suspended in air from common point by two non-conducting massless strings of same length. At equilibrium the angle between the strings is ‘α ’. The spheres are now immersed in a dielectric liquid of density $900 kg / m^{3}$ and dielectric constant 20. If the angle between the strings remains the same after the immersion, then

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Final tension is 1/20^th of initial tension

Net electric force between the spheres reduces

Mass density of the spheres is approx. $947 kg / m^{3}$

Tension in the string holding the spheres remains unchanged

answer is A, C, B.

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Detailed Solution

$Tcosθ = Μg Tsinθ = F tanθ = \frac{F}{Mg} . .... (1)$
After immersions in dielectric medium. As given no change in angle $θ$
$T^{1} sinθ = \frac{F}{\in_{r}} T^{1} cosθ = Mg [1 - \frac{ρ_{l}}{ρ_{s}}]$
$tanθ = \frac{F}{Mg (1 - \frac{ρ_{l}}{ρ_{s}}) {\in_{r}}_{}} . . . . . (2)$
From equations 1 and 2
$\frac{F}{mg} = \frac{F}{Mg [1 - \frac{ρ_{l}}{ρ_{s}}] \in_{r}} 1 - \frac{900}{ρ_{S}} = \frac{1}{20} \Rightarrow 1 - \frac{1}{20} = \frac{900}{ρ_{S}} \Rightarrow \frac{19}{20} = \frac{900}{ρ_{S}}$