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# I have a doubt, kindly clarify. Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 300 with each other. When suspended in a liquid of density 0.8 g cm-3 , the angle remains the same. If density of th

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 300 with each other. When suspended in a liquid of density 0.8 g cm-3 , the angle remains the same. If density of the material of the sphere is 1.6 g cm-3, the dielectric constant of the liquid is

• Option 1)

1

• Option 2)

4

• Option 3)

3

• Option 4)

2

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Answer is 2 of option 4

Option (4)

N

As we leant in

Coulombic force -

$\dpi{100} F\propto Q_{1}Q_{2}=F\propto \frac{Q_{1}Q_{2}}{r^{2}}=F=\frac{KQ_{1}Q_{2}}{r^{2}}$

- wherein

K - proportionality Constant

Q1 and Q2 are two Point charge

$T\cos \Theta=mg --(i)$

$T\sin \Theta=F_{e} --(ii)$

$\therefore$ from equation (i) & (ii)

$Tan \Theta=\frac{F_{e}}{mg}---(iii)$

if ball is suspended in liquid $g'=g[1-\frac{\sigma }{\rho }]$

$Tan \Theta'=\frac{F'_{e}}{mg'}$

$=\frac{f}{kmg(1-\frac{\sigma}{\rho })} --(iv)$

According to question     $\Theta'=\Theta$

from equation (iv) & (iii)

$K=\frac{1}{1-\frac{\sigma }{\rho }}$

$=\frac{\rho }{(\rho -\sigma )} =\frac{1.6}{(1.6-0.8)}=2$

$\Rightarrow$    K=2

Option 1)

1

This is incorrect option

Option 2)

4

This is incorrect option

Option 3)

3

This is incorrect option

Option 4)

2

This is correct option

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