A hollow sphere of volume V is floating on water surface with half immersed in it. What should be the minimum volume of water poured inside the sphere so that the sphere now sinks into the water?

When body (sphere) is half immersed, then Upthrust = weight of sphere⇒ V2×ρliq×g = V × ρ×g  ∴ ρ = ρliq2When body (sphere) is fully immersed then,Upthrust = weight of sphere + weight of water poured in sphere⇒ V × ρliq×g = V×ρ×g + V'× ρliq×g⇒ V ×ρliq = V × ρliq2+V'×ρliq ⇒V' = V2