Question

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of ${30}^{\circ }$ with each other. When suspended in a liquid of density $0.8gc{m}^{-3}$ the angle remains the same. If density of the material of the sphere is $1.6gc{m}^{-3}$, the dielectric constant of the liquid is

• A. $1$
• B. $4$
• C. $3$
• D. $2$

Answer 1

The correct option is D $2$

By Lami's Theorem:

$\frac{1.6Vg}{cos\left({105}^o\right)}=\frac{F}{cos\left({165}^o\right)}$

and

$\frac{0.8Vg}{cos\left({105}^o\right)}=\frac{F/k}{cos\left({165}^o\right)}$

$⟹k=2$