-->

Mechanical Properties Of Fluids

Question
CBSEENPH11020331

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

C.

2

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