Q. 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$\ 0.8\ gcm^{- 3}$, then angle remains the same. If density of the material of the sphere is $16g\ cm^{- 3},$ the dielectric constant of the liquid is
A) 4
B) 3
C) 2
D) 1
Explanation
(c) From FBD of sphere, using Lami’s theorem
$\frac{F}{mg} = \ tan\ \theta\ \ \ \ \ \ldots(i)$
When suspended in liquid, as $\theta$ remains same,
$\therefore\ \ \frac{F^{''}}{mg(1 - \frac{\rho}{d})} = \tan\theta\ \ \ \ldots(ii)$
Using Eqs. ($i$) and ($ii$)
$\frac{F}{mg} = \frac{F''}{mg\left( 1 - \frac{\rho}{d} \right)} = where,\ F^{''} = \frac{F}{k}$
$\therefore\ \ \ \ \ \ \ \frac{F}{mg} = \frac{F}{mgk\left( 1 - \frac{\rho}{d} \right)}$
0r $\ k = \frac{1}{1 - \frac{\rho}{d}} = \frac{1}{(1 - \frac{0.8}{1.6})} = 2$
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Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.