JEE Advanced2013PhysicsMechanical Properties of FluidsActual
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)
Options
- AThe net elongation of the spring is 4 π R 3 ρ g 3 k
- BThe net elongation of the spring is 8 π R 3 ρ g 3 k
- CThe light sphere is partially submerged
- DThe light sphere is completely submerged
Correct answer
A. The net elongation of the spring is 4 π R 3 ρ g 3 k
Step-by-step solution
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