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Density of a floating sphere

  1. Nov 28, 2014 #1
    1. The problem statement, all variables and given/known data
    a sphere of uniform density and radius R is floating on water , partially immersed such that the distance between the top of the sphere and the water surface is R/2
    find the density of the sphere
    2. Relevant equations
    Archimedes Principle

    3. The attempt at a solution
    One can deduce from the Archimedes Principle ,that the weight of the displaced water = the weight of the object

    ρWaterVDisplaced waterg=ρObject VObjectg

    which basically turns the problem into a mathematical problem involving finding the volume of the immersed part of the sphere.

    Consider a circle of radius R centered at the origin ,

    the required volume is ∫π(R2-x2)dx from -R to R/2 = 9πR3/8

    Thus , ρObject=(9πR3/8)/(4πR3/3) * ρWater

    =27/32 ρWater


    I dunno if it's a legitimate method . It is suggested that I utilize the concept of hydrostatic pressure instead , but i have no idea how to do that.[/SUB]
     
  2. jcsd
  3. Nov 28, 2014 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    It is legitimate and correct. The buoyant force is equal to the weight of the displaced fluid.
     
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