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 $0.8\, g\, cm^{-3}$, the angle remains the same. If density of the material of the sphere is $16\, g\, cm^{-3}$, the dielectric constant of the liquid is

• A. 4
• B. 3
• C. 2
• D. 1

Answer 1

Answer: (C)

2

Answer 2

From F.B.D of sphere, using Lami?? theorem $\frac{F}{mg} = tan\theta \quad\quad\dots\dots\dots\dots\dots\dots\left(i\right)$ when suspended in liquid, as q remains same, $\therefore\quad \frac{F'}{mg\left(1-\frac{\rho}{d}\right)} = tan\,\theta \quad\dots\dots\dots\dots\dots\dots\left(ii\right)$ using $\left(i\right)$ and $\left(ii\right)$ $\frac{F}{mg} = \frac{F'}{mg\left(1-\frac{\rho }{d}\right)}$ where, $F' = \frac{F}{K}$ $\therefore\quad \frac{F}{mg} = \frac{F'}{mg\left(1-\frac{\rho }{d}\right)}$ or $\quad K = \frac{1}{1-\frac{\rho}{d}} = 2$