A solid sphere of radius $R$ and density $\rho$ 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 $3 \rho$. The complete arrangement is placed in a liquid of density $2 \rho$ and is allowed to reach equilibrium. The correct statement(s) is (are)
Select ALL correct options:
A
the net elongation of the spring is $\frac{4 \pi R^3{ }_{\rho g}}{3 k}$
B
the net elongation of the spring is $\frac{8 \pi R^3{ }_\rho g}{3 k}$
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