In a simple pendulum experiment to determine the acceleration due to gravity ( g ), the length of the pendulum is measured as 10.0 cm using a meter scale of least count 1 mm . The time for 10 oscillations is measured as 20.0 s using a stopwatch of least count 0.1 s . The maximum percentage error in the determination of g is:

Step-by-step solution

The formula for the acceleration due to gravity g using a simple pendulum is: g = 4 ^2 L T^2 Since the time for n oscillations is t = nT , we can write T = t n . Substituting this into the formula gives: g = 4 ^2 n^2 L t^2 The maximum fractional error in g is: g g = L L + 2 t t The absolute errors are taken as the least counts of the respective measuring instruments: L = 1 mm = 0.1 cm t = 0.1 s Now, calculating the individual percentage errors: Percentage error in L = ( 0.1 10.0 ) 100 = 1 % Percentage error in t =