# Dimension problem

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

## Answers and Replies

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

brad sue
Doc Al said:
Show what you did. (Start by replacing l and g with their dimensional equivalents.)

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

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)

brad sue
Thank you SO much!

I got the solution now

Doc Al said:
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)