The period of a simple pendulum is known from experiment to be

PHYSICS · Subjective · A Level · Physics · Measurements and their errors · Measurements and their errors

Problem

T = 2\pi\sqrt{\frac{l}{g}}

. Explain in one or two sentences why dimensional analysis, although it can predict that

T \propto \sqrt{\frac{l}{g}}

, cannot fix the numerical factor

2\pi