A solid sphere of radius R and density 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. The complete arrangement is placed in a liquid of density 2 and is allowed to reach equilibrium. The correct statement(s) is (are)

Engineering

Physics

Liquid Pressure

Buoyancy

Question

A solid sphere of radius R and density $ρ$ 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 $ρ$ . The complete arrangement is placed in a liquid of density 2 $ρ$ and is allowed to reach equilibrium. The correct statement(s) is (are)

the light sphere is partially submerged

the light sphere is completely submerged.

the net elongation of the spring is $\frac{4 {πR}^{3} ρg}{3 k}$

the net elongation of the spring is $\frac{8 {πR}^{3} ρ g}{3 k}$

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If completely submerged

$F_{B} = (\frac{4}{3} {πR}^{3}) \times 2 \times 2 s = \frac{16}{3} {πR}^{3} s$

$Total mass = \frac{4}{3} {πR}^{3} 3 s + \frac{4}{3} {πR}^{3} s$

$= \frac{16}{3} {πR}^{3} s$

$∴$ kx = 4/3 $π$ R³ sg