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

 

Answers (5)

As we leant in

Coulombic force -

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

Option (4)

Right answers-3

Answer is 2 of option 4

 

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