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 \[-\,3Q.\] They are suspended from two strings of same length \[\ell \] fixed to points at the same horizontal level, hut 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) 1.8                   

D) none of these

Correct Answer: C

Solution :

[C]

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

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