Q 12-01-064JEE MainJEE Main 2024 (30 Jan, Shift 2)Medium
Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $37^\circ$ with each other. When suspended in a liquid of density $0.7\ \text{g cm}^{-3}$, the angle remains the same. If the density of the material of the sphere is $1.4\ \text{g cm}^{-3}$, the dielectric constant of the liquid is ______. $\left(\tan37^\circ = \frac34\right)$
Numerical value type. Enter your answer.
Answer: 2
In equilibrium $\tan\theta = \dfrac{F}{W}$. In the liquid the electric force becomes $F/K$ and the effective weight becomes $W(1 - \sigma/\rho)$. Same angle means
$$K = \frac{1}{1 - \sigma/\rho} = \frac{\rho}{\rho - \sigma} = \frac{1.4}{1.4 - 0.7} = 2$$
Solution by Sreeraj P, M.Sc Physics