Solving Dimension Matching Problem with Brad - 65 Characters

[brad sue]

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 don't get the soltuion right...
Thank you

brad

 

[Doc Al]

Show what you did. (Start by replacing l and g with their dimensional equivalents.)

 

[brad sue]

Show what you did. (Start by replacing l and g with their dimensional equivalents.)

L^r*L^s/T^2s equivalent to


L^r*L^s/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

 

[Doc Al]

You have T¹ = L^r*L^s*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)

 

[brad sue]

Thank you SO much!

I got the solution now

You have T¹ = L^r*L^s*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)