Acceleration due to Gravity ‘g’

Aim To Calculate the time period of a simple pendulum and use it calculate ‘g’
Apparatus  A meter rule, a stand, a metal bob, good quality string, stop clock etc
Formula  Acceleration due to gravity  g= 4\pi ^{2} \frac{L}{T^{2}}
Figure Simple Pendulum
Procedure  1. Displace the pendulum about 5º from its equilibrium position and let it swing back and forth. Measure the total time that it takes to make 10 complete oscillations. Record that time in your spreadsheet.
2. Increase the length of the pendulum by about 10 cm and repeat the measurements  made in the previous step until the length increases to approximately 1.0 m.
3. Calculate the period of the oscillations for each length by dividing the total time by the number of oscillations, 10. Record the values in the appropriate column of your data table.
4. Square the values of the period measured for each length of the pendulum and record it.
5. Graph the period of the pendulum as a function of its length. The length of the pendulum is the independent variable and should be plotted on the horizontal axis (x-axis). The period is the dependent variable and should be plotted on the vertical axis (y-axis).
6. Draw a smooth curve that best fits your data.
7. Compare your result with the accepted value of the acceleration due to gravity 9.8 m/s2
Observations  Least count of stopwatch = .……...s
S.No Length of the
pendulum (L/m)
Time for 10 oscillations (t/s) Time Period (T/s)         T2                   L/T2
1  60
2 70
3 80
4 90
5 100
Graph  Draw a graph taking lenght of the pendulum on x- axis and T2 on y-axis. The graph turns out to be a straight line. Find the gradient of the graph which is equal to T2/L.
l-t2 grapg
Calculations  L/T2 from the obsevations = ………………..
Slope of the graph = …………………….
Therefore
Acceleration due to gravity {\color{Purple} g=4\pi ^{2}}\frac{L}{T^{2}}  (from Observations)Acceleration due to gravity g=\frac{4\pi ^{2}}{slope}  (from the graph)
Precautions  1. The start and stopping of the stop-clock should be done with the least possible ‘lag’.2. The pendulum bob should be displaced parallel to the line and let ‘go’ very gently.
Result  The value of acceleration due to gravity = .……...m/s2