Question

0 the period of a pendulum is the time it takes the pendulum to swing back and forth once. if the only dimensional quantities that the period depends on are the acceleration of gravity, g, and the length of the pendulum, ℓ, what combination of g and ℓ must the period be proportional to? (acceleration has si units of m ∙ s-2.).

Answer 1

G has the dimension m/s² and l has the dimension of m

You need only seconds. You have to get rid of metres completely, so you have to divide g over l. Then you get 1/s². Finally, you raise this to the power -1/2.

Eventually you get
$T = A\sqrt{l/g}$
where A is a certain constant. Rigorous calculation show that this constant is 2π