Dimensional Reasoning Math Example 2

Solution

1. 1
   Compute $[L/g]$: $\frac{\text{m}}{\text{m}/\text{s}^2} = \text{s}^2$.
2. 2
   Compute $[\sqrt{L/g}]$: $\sqrt{\text{s}^2} = \text{s}$.
3. 3
   Compute $[2\pi\sqrt{L/g}]$: $2\pi$ is dimensionless, so the result has units of seconds.
4. 4
   The period $T$ should be in seconds. The formula is dimensionally consistent.