1. Steel has a density of 8 g/cm3. Let\'s think about building a spherical shell

Question

1. Steel has a density of 8 g/cm3. Let's think about building a spherical shell, made out of a few cnm 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

let R = 1 m

let r is the inner radius.

volume of the shell, V = (4/3)*pi*R^3

mass of the shell, m = density*effective volume

= rho_stell*(4/3)*pi*(R^3 - r^3)

In the equilibrium

Boynat force = weight of the shell

(rho_water)*(V/2)*g = m*g

1000*((4/3)*pi*R^3)*(1/2) = rho_stell*(4/3)*pi*(R^3 - r^3)

1000*(2/3)*pi*1^3 = 8000*(4/3)*pi*(1^3 - r^3)

on solving the avove equation we get,

r = 0.9787 m

so, thickness of the shell = R - r

= 1 - 0.9787

= 0.0213 m

= 2.13 m

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