Question

A hollow steel sphere (the density of steel is 7820 kg/m³) with an internal diameter of 10 cm and a thickness of 7mm is attached to a wooden cylinder (the wood has a density of 900 kg/m³) with a length 50 cm and a diameter of 20 cm. The inside of the sphere is filled with a fluid. If the system is neutrally buoyant in water with a density of 998.2 kg/m³, determine the density of the fluid inside the steel sphere.

Answer 1

System is neutrally buoyant.

∴ Average density of system = average density of water

Let m₁, ρ₁ and V₁ be the mass, density and volume of steel sphere respectively

Let m₂, ρ₂ and V₂ be the mass, density and volume of steel sphere respectively

Let m₃, ρ₃ and V₃ be the mass, density and volume of steel sphere respectively

Total mass of system  

  

Total volume of system

For hollow sphere,

inner radius = = 0.05m

outer radius = = + thickness = 0.05+0.007 = 0.0057 m

volume of solid part of cylinder

  

Volume of fluid = volume of hollow region of sphere

  

  

Volume of cylinder

  

By given condition,

Average density of system = average density of water

so, the density of fluid is