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Homework Help: Dimension problem

  1. Sep 4, 2005 #1
    Hi,

    I have a problem about dimension matchig.

    the dimensional relation between the period τ , the pendul length l, and the acceleration of the gravity g takes the form:
    [ τ ]=[l^r] [g^s]

    Use the fact that the dimendion of τ is [T], that of l is [L], and that of g is [L/T^2] to show that

    τ is proportional to (l/g)^(1/2)

    I dont get the soltuion right...
    Thank you

    brad
     
  2. jcsd
  3. Sep 4, 2005 #2

    Doc Al

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    Staff: Mentor

    Show what you did. (Start by replacing l and g with their dimensional equivalents.)
     
  4. Sep 4, 2005 #3
    Lr*Ls/T2s equivalent to


    Lr*Ls/T-2s . from here I get lost in my calculation I tried to separated the exponent of T into T-s*T-s but really it does not make sense to me.
    please give me some hint so I can go further

    Thank
    Brad
     
  5. Sep 4, 2005 #4

    Doc Al

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    Staff: Mentor

    You have T1 = Lr*Ls*T-2s. So now you can set up equations for the exponents:
    1 = -2s
    0 = r + s (note that having no L factor is equivalent to having L0)
     
  6. Sep 4, 2005 #5
    Thank you SO much!!

    I got the solution now

     
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