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 $0.8{\text{g /cm}}^3$, the angle remains the same. If density of the marterial of the sphere is $1.6{\text{g /cm}}^3$, then dielectric constant of the liquid is

• A. $4$
• B. $3$
• C. $2$
• D. $1$

Answer 1

The correct option is C $2$

Step 1 .Drawing FBD

From free body diagram,

$F_e=Tsin{15}^o.....\left(1\right)$

$mg=Tcos{15}^o......\left(2\right)$

from eq(1) and (2)

$tan{15}^o=\frac{F_e}{mg}............\left(i\right)$

I

In liquid, $F_e^{\prime }=Tsin{15}^o......\left(3\right)$

$mg=F_B+Tcos{15}^o$ .......(4)