Answer: √(L/g)
Explanation:
Here we only work with the units:
The unit of the period is units of time, so we have:
[T] = [s]
Now, the units of the length of the pendulum are units of distance:
[L] = [m]
And the units of the acceleration are:
[g] = [m/s^2]
Now, we want to work with those two in such way that the end result is only in seconds.
First, we can see that in g we have seconds square, so we know that we should use a square root.
Then we can divide L by g in order to remove the distance unit, and to have the time unit in the numerator
[L/g] = [m*s^2/m] = [s^2]
Now we apply the square root:
[√(L/g)] = [√s^2] = [s]
Then the combination is: √(L/g)
T = k*√(L/g)
where k is the constant of proportionality.
