The period T of a simple pendulum is related to its length l by the equation:

T = 2π√I/g
Where g is the acceleration of free fall.
a. A graph is plotted with T² on the y-axis and l on the x-axis. Express the gradient in terms of g.
b. A student measures the time t for 10 oscillations for different lengths l.
This table shows her data.

i. Calculate and record values of T and T², including the absolute uncertainties in T and T².
ii. Plot a graph of T²/s² against l/m including error bars for T².
iii. Draw a straight line of best fit and a worst acceptable line on your graph.
iv. Determine the gradient of your line and include the uncertainty in your answer.
v. Use your value of the gradient to determine g and include the absolute uncertainty in your value.
vi. Using your value of g and its uncertainty, calculate the value of t when the length l is 0.900 m. Include the absolute uncertainty in your answer.

Transcribed Image Text:

1/ m t/ s T. T2 0.300 11.1 + 0.1 0.400 12.8 + 0.1 0.500 14.2 + 0.1 0.600 15.8 ± 0.1 0.700 16.9 ± 0.1 0.800 18.1 ± 0.1 Table P2.6