Accuracy and differentiation

[aruwin]

To get the value of g, the period(T), length of pendulum (l) and radius of pendulum bob (a) were measured.
Well, my question is actually to find which accuracy of one of these measurements need to be improved?
The formulae given to find the probable error are
ε _gT = (partial differentiation of g in respect to T) X ε _T

ε _gl = (partial differentiation of g in respect to l) X ε _l

ε_ga = (partial differentiation of g in respect to a) X ε _a

After calculating, the values were:
ε _gT = 1.1 X 10^-3
ε _gl = 3.5 X 10^-4
ε _ga = 6.9 X 10^-5

Since the ε _gT has the biggest derivative, I think T's accuracy is the one that needs the most improvement. Am I right or wrong?

 

[D H]

You're right. However, your value of l is also pretty noisy. Improve your measurements of T by an order of magnitude and now it is your l value that will be the primary culprit.

 

[aruwin]

Improve your measurements of T by an order of magnitude .

What do you mean by this?