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Question

# A solid sphere of radius R and density ρ is attached to one end of a mass-less 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 light sphere is partially submerged
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B
The net elongation of the spring is 4πR3ρg3k
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C
The light sphere is completely submerged
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D
The net elongation of the spring is 8πR3ρg3k
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Solution

## The correct option is C The light sphere is completely submergedAt equilibrium, for upper sphere kx+43πR3ρg=43πR3(2ρ)g ⇒x=4πR3ρg3k The system is completely submerged as total weight = Total Buoyant force.

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