A solid sphere of radius \( R \) and density \( \rho \) is attached to one end of a mass-less sp....

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A solid sphere of radius \( R \) and density \( \rho \) is attached to one end of a mass-less spring of force constant \( k \). The
\( \mathrm{P} \)
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)
(1) The net elongation of the spring is \( \frac{4 \pi R^{3} \rho g}{3 k} \)
(2) The net elongation of the spring is \( \frac{8 \pi R^{3} \rho g}{3 k} \)
(3) The light sphere is partially submerged
(4) The light sphere is completely submerged


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