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 . The spheres are now immersed in a dielectric liquid of density 800 kg m−3 and dielectric constant 21. If the angle between the strings remains the same after the immersion, then

The net electric force on any sphere is lesser but by Coulomb law the force due to one sphere to another remain the same.In equilibrium Tcos⁡α2=mg and Tsin⁡α2=FDividing, tanα2=mgFAfter immersion in dielectric liquid, as given, there is no change in angle α So Tcos⁡α2=mg−Vρg when ρ=800Kg/m3 and Tsin⁡α2=Fer∴mgF=mg−VρgFer⇒1er=1−ρdd= density of sphere ⇒121=1−800d⇒d=840

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 . The spheres are now immersed in a dielectric liquid of density 800 kg m−3 and dielectric constant 21. If the angle between the strings remains the same after the immersion, then

The net electric force on any sphere is lesser but by Coulomb law the force due to one sphere to another remain the same.In equilibrium Tcos⁡α2=mg and Tsin⁡α2=FDividing, tanα2=mgFAfter immersion in dielectric liquid, as given, there is no change in angle α So Tcos⁡α2=mg−Vρg when ρ=800Kg/m3 and Tsin⁡α2=Fer∴mgF=mg−VρgFer⇒1er=1−ρdd= density of sphere ⇒121=1−800d⇒d=840

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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 𝛼. The spheres are now immersed in a dielectric liquid of density 800 kg m⁻³ and dielectric constant 21. If the angle between the strings remains the same after the immersion, then

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electric force between the spheres remains unchanged

electric force between the spheres reduces

mass density of the spheres is 840 kg m⁻³

the tension in the strings holding the spheres remains unchanged

answer is A, C.

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Detailed Solution

The net electric force on any sphere is lesser but by Coulomb law the force due to one sphere to another remain the same.

In equilibrium

$\begin{array}{l} Tcos \frac{α}{2} = mg \\ and Tsin \frac{α}{2} = F \end{array}$

$D i v i d i n g, \tan \frac{α}{2} = \frac{m g}{F}$

After immersion in dielectric liquid, as given, there is no change in angle $α$

$\begin{array}{l} So Tcos \frac{α}{2} = mg - V ρ g \\ when ρ = 800 Kg / m^{3} \\ and Tsin \frac{α}{2} = \frac{F}{e_{r}} \\ ∴ \frac{mg}{F} = \frac{mg - V ρ g}{\frac{F}{e_{r}}} \end{array}$

$\begin{array}{l} \Rightarrow \frac{1}{e_{r}} = 1 - \frac{ρ}{d} \\ d = density of sphere \\ \Rightarrow \frac{1}{21} = 1 - \frac{800}{d} \\ \Rightarrow d = 840 \end{array}$