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)

A

the net elongation of the spring is $$\frac{4 \pi R^3 \rho g}{3k}$$

B

the net elongation of the spring is $$\frac{8 \pi R^3 \rho g}{3k}$$

C

the light sphere is partially submerged.

D

the light sphere is completely submerged.