A cubical block of volume v and density $3 ρ$ is placed inside a liquid of density $ρ$ and attached to a spring of spring constant k as shown in the figure. Assuming ideal spring and pulley and spring is attached at A which is at R/2 from centre. The compression in the spring at equilibrium is :

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Block weight: 3 ρ vg Buoyancy: ρ vg Rope tension at equilibrium: T = 3 ρ vg − ρ vg = 2 ρ vg Take moments about the disk centre: the rope acts at radius R and the spring at R/2. TR = ( k x ) 2 R ​ Therefore: x = k 2 T ​ = k 4 ρ vg ​

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