A simple pendulum consists of a small, heavy ball of mass $m$ at the end of a long string of length $L$. The period of the pendulum should depend on these factors, as well as gravity, which is the driving force for making it move. What information can you get about the relationship between these variables from a consideration of their dimensions? Suppose you measured the period, $T_{1}$, of a pendulum with mass $m_{1}$ and length $l_{1}$. How could you use this to determine the period of a different pendulum with a different mass and length? What would be the ratio of the pendulum period on the moon to that on the earth? How could you use the pendulum to determine the variation of $g$ on the earth's surface?