Steel has a density of 8 g/cm3 . Let’s think about building a spherical shell, m

Question

Steel has a density of 8 g/cm3 . Let’s think about building a spherical shell, made out of a few cm thick steel that floats in water. How thick would you have built the wall of this perfectly spherical shell with an outer diameter of 2m, so that the shell will float in water in such a way that exactly ½ of the shell is under water and ½ of the shell is above water. This means that the complete shell should have the mass of the water the shell displaces. Can you show that the steel can be approximately 2.2cm thick?

Explanation / Answer

Gravitational force due to weight of whole shell= Buoyancy force due to water displaced by half shell

So, 8000kg/m^3 * 4(2^3-r^3) / 3 m^3 * 9.8m/s^2 = 1/2 * 4*2^3 / 3 m^3* 1000 kg/m^3 * 9.8m/s^2

Or, 8*(8-r^3) = 0.5*8

So, r= 1.957m . So the thickness of steel is 2m-1.957m= 0.0426m = 4.26cm

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