question_answer

Two identical spheres of same mass and specific gravity (which is the ratio of density of a substance and density of water) 2.4 have different charges of Q and\[-\,3\,Q\]. They are suspended from two string of same length \[\ell \] fixed to points at the same horizontal level, but distant \[\ell \] from each other. When the entire set up is transferred inside a liquid of specific gravity 0.8, it is observed that the inclination of each string in equilibrium remains unchanged. Then the dielectric constant of the liquid is

A) 2

B) 3

C) 1.5

D) None of these

Correct Answer: C

Solution :

\[\tan \theta =\frac{{{F}_{e}}}{V\rho g}=\frac{{{F}_{e}}/k}{V\,(\rho -\sigma )g}\]

\[\Rightarrow \]   \[k=\frac{\rho }{\rho -\sigma }=\frac{2.4}{2.4-0.8}=1.5\]

Ans.     \[k=\frac{\rho }{\rho -\sigma }=\frac{2.4}{2.4-0.8}=1.5\]