In an experiment to determine the acceleration due to gravity ( g ) using a simple pendulum, the length of the pendulum is measured as 20.0 cm using a scale of least count 1 mm . The time for 50 oscillations is measured as 100 s using a stopwatch of least count 1 s . The maximum percentage error in the determination of g is:

Step-by-step solution

The formula for acceleration due to gravity using a simple pendulum is: g = 4 ^2 L T^2 The maximum percentage error in g is given by: g g 100 = L L 100 + 2 ( T T 100 ) For the length measurement: Measured length, L = 20.0 cm Least count, L = 1 mm = 0.1 cm Percentage error in length = 0.1 20.0 100 = 0.5 % For the time measurement: Total time measured, T_ total = 100 s Least count, T_ total = 1 s Percentage error in time = 1 100 100 = 1 % Substituting these into the error equation for g : g g 100 = 0.5 % + 2(1 %) = 0