Using dimensional analysis, find the correct relation for time period $T$ of a simple pendulum:

Assume $T\propto L^a g^b$. Then $[T]=[L]^a[LT^{-2}]^b=[L^{a+b}T^{-2b}]$. Matching powers gives $-2b=1\Rightarrow b=-\frac12$, and $a+b=0\Rightarrow a=\frac12$. So $T\propto \sqrt{L/g}$.