The period T of a simple pendulum depends on the length L of the pendulum and the acceleration of gravity g (dimensions L/T²). 

(a) Find a simple combination of L and g which has the dimensions of time. 

(b) Check t he dependence of the period T on the length L by measuring the period (time for a complete swing back and forth) of a pendulum for two different values of L. 

(c) The correct formula relating T to L and g involves a constant that is a multiple of π, and cannot be obtained by the dimensional analysis of part (a). It can be found by experiment as in (b) if g is known. Using the value g = 9.81 m/s² and your experimental results from (b), find the formula relating T to L and g.