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Homework Help: Find how hollow a rock is given its density and its weight in water!

  1. Sep 27, 2010 #1
    1. The problem statement, all variables and given/known data

    A geologist thinks a rock is hollow. The rock weighed in air is twice as much as when it's in water. Find the fraction of the rock's volume that is solid given the solid part of the rock is 2500kg/m^3 and water is 1000kg/m^3


    2. Relevant equations

    rho = mass/volume
    Fb = rho*volume*gravity
    F(normal) = Force gravity (rock in air) - rho(fwater)*V(displaced)*gravity

    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 27, 2010 #2
    Can you please show your attempt at the solution as per PF guidelines.

    Jared
     
  4. Oct 6, 2010 #3
    Given that density of solid part of rock is 2500kg/m^3, water is 1000kg/m^3, air has neglibile density and the whole object weighs twice is much in air than in water:

    Apparent weight = m(object in air)*g - m(fluid displaced)*g
    1/2*m(object in air)*g = m(object in air)*g - m(fluid displaced)g
    1/2* rho (object)*V*g = rho (object)*V*g - rho (fluid)*V*g
    1/2* rho (object) = rho (object) - rho (fluid)
    -1/2*rho (object) = - 1000kg/m^3
    rho (object) = 2000kg/m^3

    therefore
    2000kg/m^3 = x*(solid part) + (1-x)*(air)
    2000kg/m^3 = 2500kg/m^3*x
    x = 2000/2500 = 0.8 or 80%
     
  5. Oct 6, 2010 #4

    rl.bhat

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    Homework Helper

    Your answer is correct.
     
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