The period, T, of a pendulum is related to the pendulum's length, L and the constant acceleration of gravity, g, by the equation


A student has measured the period of a pendulum for various lengths and wants to linearize the data to extract directly the acceleration of gravity as the slope of a straight line. To get this straight line, the student must ...
Answer

Plot L / T2 vs. 4π2

Plot g T2 vs. 4π2 L

Plot T vs. 2πL1/2

Plot T2 vs. 4π2 L

Plot 4π2 L vs. T2

T = 2 pi sqrt (L/g)

T^2 = 4 pi^2 L / g

g = 4 pi^2 L/T^2
(your final choice)

To linearize the data and extract the acceleration of gravity as the slope of a straight line, the student must plot T2 (period squared) on the y-axis and 4π2L (four times pi squared times length) on the x-axis.

This can be done by following these steps:

1. Measure the period of the pendulum for different lengths.
2. Square the measured periods to obtain T2.
3. Multiply the length of each pendulum by 4π2.
4. Plot T2 on the y-axis and 4π2L on the x-axis.
5. When the data points are plotted, they should form a straight line.
6. Calculate the slope of this line, which corresponds to the acceleration of gravity, g.

Therefore, the correct answer is to plot T2 vs. 4π2 L.