Experimental Measurement of the Gravitational Acceleration Using a Simple Pendulum at Sites Across Bauchi State

The precise local value of gravitational acceleration is an important geophysical parameter with applications in structural engineering, geodesy, and precision navigation. This study determines the local gravitational acceleration at five sites across Bauchi State, North East Nigeria, using the simple pendulum method. A brass pendulum bob suspended on a non-elastic nylon thread was used for measurements at each site, with pendulum lengths varying from 50 cm to 100 cm in 10 cm increments. Thirty complete oscillations were timed using a digital stopwatch for each length setting, and the experiment was repeated ten times per length to minimize random error. The period squared versus pendulum length regression method was applied to derive the local gravitational acceleration from the slope of the best-fit line. Measured values of g ranged from 9.789 m/s2 at the elevated Bauchi Township station to 9.796 m/s2 at the lower-altitude Ningi site, consistent with the expected latitude and altitude corrections to the standard sea-level value of 9.80665 m/s2. The study applies the theoretical correction formula accounting for local latitude (10.3 degrees North) and elevation above sea level to validate measured values against predicted free-air anomaly corrections. Differences between measured and predicted values were within 0.04 percent, well within the experimental uncertainty budget. The study demonstrates a reliable, low-cost protocol for measuring local gravity variations and contributes site-specific data to Nigeria's sparse gravity database. Keywords: gravitational acceleration, simple pendulum, Bauchi State, local gravity, geophysics