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To find the density of a material of the body using moments

  1. Jul 25, 2009 #1
    1. The problem statement, all variables and given/known data
    "[URL=http://img193.imageshack.us/my.php?image=63378846.png[/URL]
    Fig.A shows the balanced position of a light rod carrying an object X and a mass M .
    Fig.B shows the balanced position of the same system when X is immersed in water.If the density of water is d,the density of the material made of X is given by,
    1) [L[SUB]1[/SUB]/(L[SUB]1[/SUB]-L[SUB]2[/SUB])]d 2) (L[SUB]1[/SUB]/L[SUB]2[/SUB])d 3) [L[SUB]1[/SUB]/L[SUB]1[/SUB]+L[SUB]2[/SUB]]d 4) [(L[SUB]1[/SUB]-L[SUB]2[/SUB])/L1]d 5) (L[SUB]2[/SUB]/L[SUB]1[/SUB]) d

    [b]2. Relevant equations[/b]



    [b]3. The attempt at a solution[/b]
    Taking moments about the pivot,
    for A
    mg*l = Mg*L[SUB]1[/SUB]
    m=ML[SUB]1[/SUB]/l m=mass of X

    for B
    Mg*L[SUB]2[/SUB] = m[SUB]1[/SUB]g*l
    m[SUB]1[/SUB]= ML[SUB]2[/SUB]/l m[SUB]1[/SUB]g = apparent weight of X in water

    density of X= (real weight/apparent loss of weight in water) d
    =(m/m-m[SUB]1[/SUB])*d
    =(1-m/m[SUB]1[/SUB])d
    =(1-L[SUB]1[/SUB]/L[SUB]2[/SUB])*d
    gives me( L[SUB]2[/SUB]-L[SUB]1[/SUB]/L[SUB]2[/SUB])*d, which is not even among the choices given.
    I can't figure out where I'm going wrong.
     
    Last edited by a moderator: Apr 24, 2017
  2. jcsd
  3. Jul 25, 2009 #2

    alphysicist

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    Homework Helper

    Hi leena19,

     
    Last edited by a moderator: Apr 24, 2017
  4. Jul 25, 2009 #3
    Thanks for replying!
    Oops!
    after correcting it ,I get
    [L1/(L1-L2)]d which would be answer no.1,hopefully?


    EDIT:
    The answer is (1).
    Thank you very much for the help!
     
    Last edited: Jul 25, 2009
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