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Sphere floating in liquid

  1. Oct 8, 2011 #1
    1. The problem statement, all variables and given/known data
    A hollow spherical shell of external diameter of 1 metre and uniform thickness of 0.2m floats in a liquid with half its volume immersed. If the relative density is 1.5 find t 2 decimal places the relative density of the material of the shell.


    2. Relevant equations
    Buoyancy = Vρg = Weight


    3. The attempt at a solution

    Relative density of liquid = 1.5
    Density of liquid = 1500

    Since it floats Buoyancy = Weight

    Vρg = Vρg

    ( [itex]\frac{2}{3}[/itex][itex]\pi[/itex] ) (1500g) = [ [itex]\frac{4}{3}[/itex] [itex]\pi[/itex] - [itex]\frac{4}{3}[/itex] [itex]\pi[/itex] (0.8[itex]^{3}[/itex]) ) ] Xg

    1000[itex]\pi[/itex] g = [itex]\frac{244}{375}[/itex] [itex]\pi[/itex] Xg

    1000 = [itex]\frac{244}{375}[/itex] X

    X = 1536.8

    Therefore relative density = 1.5

    Answer = 0.96
     
  2. jcsd
  3. Oct 8, 2011 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    4/3 is missing from the right-hand side. It should be 1000=(4/3)*(244/375)*X.

    ehild
     
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