In an experiment to determine the acceleration due to gravity ( g ) using a simple pendulum, the length of the pendulum is measured as 25.0 cm using a scale of least count 0.5 cm. 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 acceleration due to gravity g using a simple pendulum is given by: g = 4 ^2 L T^2 If t is the total time for n oscillations, then T = t n . Substituting this, we get: g = 4 ^2 n^2 L t^2 The maximum percentage error in g is: g g 100 = L L 100 + 2 ( t t 100 ) Given values: L = 25.0 cm, L = 0.5 cm t = 100 s, t = 1 s Calculating individual percentage errors: L L 100 = 0.5 25.0 100 = 2 % t t 100 = 1 100 100 = 1 % Therefore, the maximum percentage error in g is: g g 100 = 2 % + 2(1 %) = 4 % Answer: 4