Problem: 1707071: Mechanical Properties of Liquid

A solid sphere of radius R and density d 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 3d. The complete arrangement is placed in a liquid of density 2d and is allowed to reach equilibrium. The net elongation of the spring is ____.

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At equilibrium- \[\frac{4}{3}\pi R^{3}2dg=\frac{4}{3}\pi R^{3}dg+T\]
\[\Rightarrow T=\frac{4}{3}\pi R^{3}dg\]
\[\therefore \Delta l=\frac{T}{K}=\frac{4}{3K}\pi R^{3}dg\]