1)

A solid sphere of radius R and density ρ  is attached to one end of a massless spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density 3ρ. The complete arrangement is placed in a liquid of density 2ρ  and is allowed to reach equilibrium. The correct statement(s) is (are)


A) the net elongation of the spring is 4πR3ρg3k

B) the net elongation of the spring is 8πR3ρg3k

C) the light sphere is partially submerged

D) the light sphere is completely submeged

Answer:

Option A,D

Explanation:

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 On small sphere

  43πR3(ρ)g+kx=43πR3(2ρ)g    ......(i)

  On second sphere (large)

  43πR3(3ρ)g=43πR3(2ρ)g+kx   .....(ii)

 By Eqs. (i) and (ii) , we get

    x= 4πR3ρg3k