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A solid sphere of radius R and density $ρ$ is attached to one end of amass less spring of force constant K. The other end of the spooning is connected to another solid sphere of radius R and density $3 ρ$ . The whole system is placed in a liquid of density $2 ρ$ and is allowed to reach equilibrium. Then

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the net elongation of the spring is

\frac{8 π R^{3} ρ g}{3 k}

the net elongation of the spring is

\frac{4 π R^{3} ρ g}{3 k}

the light sphere is completely submerged

the light sphere is partially submerged

answer is A, D.

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Detailed Solution

F.B.D of Sphere (1)

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$mg + k x = F_{b}$

$v ρ_{1} g + k x = v ρ_{2} g$

$\frac{4}{3} π R^{3} ρ g + k x = \frac{4}{3} π R^{3} (2 ρ) g$

$k x = \frac{4}{3} π R^{3} ρ (2 - 1)$

$x = \frac{4}{3} π R^{3} ρ$

$x = \frac{4}{3} \frac{π R^{3} ρ}{k}$

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