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

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 2ρ and is allowed to reach equilibrium. The correct statement(s) is (are)

TestHub · Accepted Answer

kx + f B = mg From equilibrium of sphere. 3 ρ kx + 2 ρ vg - 3 ρ vg kx = ρ vg x = ρ vg k = ρ g 4 3 π R 3 ρ vg k = ρ g 4 3 π R 3 K Let v 1 = volume submerged of lighter sphere. kx + mg = F B ρ vg + ρ vg = 2 ρ v 1 g = 2 ρ vg = 2 ρ v 1 g ⇒ v 1 = v

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