The period t of a simple pendulum depends
on the length l of the pendulum and the acceleration of
gravity g (dimensions l/t^2). (a) find a simple combination of
l and g that has the dimensions of time. (b) check the
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 pi, and cannot be obtained by the dimensional
analysis of part (a). it can be found by experiment as in
part (b) if g is known. using the value g = 9.81 m/s² and your
experimental results from part (b), find the formula relating t
to l and g.

Researchers conducted an experiment to identify the effects of three different hand sanitizers on the growth of bacteria. the researchers grew one type of bacteria in twenty-four identical covered petri dishes. then, they opened eighteen petri dishes and applied the three hand sanitizers to six petri dishes each. they left the remaining six petri dishes closed as a control group. when the researchers measured the growth of bacteria two days later, the six dishes that had no hand sanitizer showed the least amount of bacterial growth. the researchers concluded that not using any hand sanitizer would lead to the least bacterial growth. which statement best explains why the researchers’ conclusion was not justified? the experiment tested too many variables. the control group was not treated the same as the experimental group. the sample size of twenty-four petri dishes is not large enough. the single type of bacteria is not adequate to make any conclusions.