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Two identical charged spheres are suspended by strings of equal length. The strings makes an angle of $30 º$ with each other. When suspended in a liquid of density $0.8 g c c^{- 1}$ , the angle remains the same. The dielectric constant of the liquid is [Density of sphere material is $1.6 g c c^{- 1}$ ]

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answer is B.

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Detailed Solution

$M^{'} g = m g (1 - \frac{1}{1.6} \times 0.8)$

$= m g (1 - \frac{1}{2}) = \frac{m g}{2}$

$T \cos θ = m g; T \sin θ = F$

$Tan θ = \frac{F}{m g}; Tan θ = \frac{F}{M^{'} g}$

When suspended in liquid $Tan θ = \frac{F / K}{m g / 2} \Rightarrow K = 2$

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