Plotting a Graph of T² Against L to Determine the Value of g

Physics Practical: Determining Acceleration Due to Gravity (g)

Aim:

To determine the value of gravitational acceleration (g) by plotting a graph of \( T^2 \) against Length (L) using a simple pendulum.

Apparatus:

• Clamp stand and clamp
• String
• Pendulum bob
• Ruler or meter rule
• Stopwatch
• Graph paper (or plotting software)

Procedure:

1. Set up the pendulum so that it swings freely from a fixed point.
2. Measure and record the length L of the string from the point of suspension to the center of the bob.
3. Displace the bob slightly and release to allow it to swing.
4. Measure the time for 10 oscillations, repeat for accuracy.
5. Calculate the time period T = Total Time / 10.
6. Compute \( T^2 \) for each length.
7. Plot a graph of \( T^2 \) (Y-axis) against L (X-axis).
8. Determine the slope (m) of the straight-line graph.
9. Use the formula: \[ T^2 = \frac{4\pi^2}{g}L \Rightarrow g = \frac{4\pi^2}{\text{slope}} \]

Graph Example:

NECTA-Style Example 1:

Given the lengths and times for 10 oscillations below:

  Length (cm): 20, 30, 40, 50, 60
  Time for 10 swings (s): 9.0, 11.0, 12.8, 14.1, 15.6
  

Steps:

• Convert lengths to meters: 0.2, 0.3, 0.4, 0.5, 0.6
• Compute T = Time/10, then T^2
• Plot T^2 vs L and find slope
• Use slope to compute g

NECTA-Style Example 2:

In a NECTA exam, a candidate recorded the following:

  Lengths (m): 0.25, 0.35, 0.45, 0.55
  Periods (T in s): 1.00, 1.18, 1.34, 1.49
  

• Compute T^2 values
• Plot graph, find slope
• g = 4π² / slope

Video Tutorial: