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    Attachment 503891503893T=2π squareroot(1/g)
    T=2π squareroot(m/k)
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    Pls help me fast
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    Do they all have the same units?
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    Please.... I'm doing OCR B at AS level and am looking for good revision sites. I have the CGP book but as everyone can guess.. I need an A so that my school write a fantastic reference
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    (Original post by Kyx)
    Do they all have the same units?
    No they don't
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    Pls hurry guys, I need to complete it tomorrow. (The symbols have their usual meaning) for example m=mass T=seconds
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    have you been taught anything about this?

    for these dimensional homogeneity questions you have to think in terms of the dimension rather than the unit system...
    L is length
    T is time (not seconds, seconds is the SI unit for measuring time)
    M is mass


    so for
    a) T=2π (l/g)1/2

    you can kick out the 2π immediately because it's dimensionless

    T=(l/g)1/2
    T2=l/g

    now start to put it into the dimensional notation
    the dimension of T is T
    the dimension of l is L
    the dimension of g in basic dimensions (and the dimension of any acceleration) is L T-2 (might help to think about the units acceleration is measured in)

    so in dimensional notation we've got
    T2=L / L T-2

    cancel the Ls
    T2=1/T-2
    so
    T2=T2
    T=T ...which is what we're asked for.


    NB not all constants are dimensionless so you've got to include the dimensions of (for example) spring constants & the gravitational constant.
 
 
 
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