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Question

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 (4πR3ρg)3k

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B

The net elongation of the spring is (8πR3ρg)3k

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C

The light sphere is partially submerged.

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D

The light sphere is completely submerged.

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Solution

The correct options are
A

The net elongation of the spring is (4πR3ρg)3k


D

The light sphere is completely submerged.



Here, T=kx
For upper sphere at equilibrium, kx+43πR3ρg=43πR32ρgx=43kπR3ρg
The system is completely submerged as total weight is balanced by total buoyant force.


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