Question

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 30º 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

4

3

2

1

Solution

From FBD of sphere, using Lami theorem

F/Mg = Tan θ .... (i)
when suspended in liquid as θ remains unchanged,
$therefore space fraction numerator straight F apostrophe over denominator mg space open parentheses 1 minus begin display style straight rho over straight d end style close parentheses end fraction space equals space tan space straight theta space... left parenthesis ii right parenthesis Using space eqs. space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma space we space get straight F over mg space equals space fraction numerator straight F apostrophe over denominator mg space open parentheses 1 minus begin display style straight rho over straight d end style close parentheses end fraction comma space where space straight F apostrophe space equals space straight F over straight K therefore space space straight F over mg space equals space fraction numerator straight F over denominator mgK space open parentheses 1 minus begin display style straight rho over straight d end style close parentheses end fraction space or straight K space equals space fraction numerator 1 over denominator 1 minus begin display style straight rho over straight d end style end fraction space equals space fraction numerator 1 over denominator open parentheses 1 minus begin display style fraction numerator 0.8 over denominator 1.6 end fraction end style close parentheses end fraction space equals space 2$

Some More Questions From Mechanical Properties of Fluids Chapter

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Mechanical Properties Of Fluids

Some More Questions From Mechanical Properties of Fluids Chapter

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What is the nature of inter-atomic or inter-molecular forces?

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Define rigid body.

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What is elasticity?

Name the property of material that opposes the deformation in it.

Name the quantity which has neither unit nor dimensions.

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