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Fluid problem

  1. Feb 22, 2009 #1
    1. The problem statement, all variables and given/known data
    metal cube is placed in an empty vessel. When water is
    filled in the vessel so that the cube is completely immersed in the
    water, the force on the bottom of the vessel in contact with the
    cube:
    (a) Will decrease
    (b) Will increase
    (c) Will remain same
    (d) Will become zero

    i tried the ans i think it's (a) will decrease.but book say's (c)it remains constant
    2. Relevant equations



    3. The attempt at a solution
    Consider the two cases case1) when vessel is empty
    Case2) when vessel is filled with water
    Let w=weight of the metal cube (in air)
    N=normal reaction exerted by cube on the vessel in absence of water
    R= normal reaction exerted by cube on the vessel in presence of water
    B= Buoyancy force (=weight of fluid displaced by the block)
    Then by drawing the free body diagram of metal cube in each case as shown in fig. above we have
    Case 1)w=N
    Case 2)w=R+B
    i.e. R=w-B. Thus the reaction on cube(by the vessel) in presence of water decreases due to the Buoyant force. Hence, the force on the bottom of the vessel in contact with the cube decreases
     
  2. jcsd
  3. Feb 24, 2009 #2
    I agree with your answer and not that of the book. Maybe we're missing something?
     
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